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ANRV305-PU28-05                                                                           ARI      6 March 2007       17:8




                                                                                                                                            Network Analysis in Public
                                                                                                                                            Health: History, Methods,
                                                                                                                                            and Applications
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                                                                            Douglas A. Luke and Jenine K. Harris
                                                                                                                                            Department of Community Health, School of Public Health, Saint Louis University,
                                                                                                                                            St. Louis, Missouri 63104; email: dluke@slu.edu
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         Annu. Rev. Public Health 2007. 28:69–93            Key Words
                                                                                         The Annual Review of Public Health is online at    social networks, disease transmission, diffusion of innovations,
                                                                                         http://publhealth.annualreviews.org
                                                                                                                                            social support, social capital
                                                                                         This article’s doi:
                                                                                         10.1146/annurev.publhealth.28.021406.144132        Abstract
                                                                                         Copyright c 2007 by Annual Reviews.                Network analysis is an approach to research that is uniquely suited
                                                                                         All rights reserved
                                                                                                                                            to describing, exploring, and understanding structural and relational
                                                                                         0163-7525/07/0421-0069$20.00                       aspects of health. It is both a methodological tool and a theoretical
                                                                                         First published online as a Review in Advance on   paradigm that allows us to pose and answer important ecological
                                                                                         January 12, 2007                                   questions in public health. In this review we trace the history of
                                                                                                                                            network analysis, provide a methodological overview of network
                                                                                                                                            techniques, and discuss where and how network analysis has been
                                                                                                                                            used in public health. We show how network analysis has its roots
                                                                                                                                            in mathematics, statistics, sociology, anthropology, psychology, biol-
                                                                                                                                            ogy, physics, and computer science. In public health, network anal-
                                                                                                                                            ysis has been used to study primarily disease transmission, especially
                                                                                                                                            for HIV/AIDS and other sexually transmitted diseases; information
                                                                                                                                            transmission, particularly for diffusion of innovations; the role of
                                                                                                                                            social support and social capital; the influence of personal and social
                                                                                                                                            networks on health behavior; and the interorganizational structure
                                                                                                                                            of health systems. We conclude with future directions for network
                                                                                                                                            analysis in public health.



                                                                                                                                                                                                      69
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                                                                                                      INTRODUCTION                                          Network analysis, then, is the field that
                                                                                                                                                         concerns itself with relational data and re-
                                                                                                      Over the past several decades researchers
                                                                                                                                                         search questions. More specifically, the net-
                                                                                                      have placed increasing emphasis on using eco-
                                                                                                                                                         work paradigm has four important features
                                                                                                      logical models and methods in the health
                                                                                                                                                         (51):
                                                                                                      and social sciences in general, and public
                                                                                                      health in particular. The 2001 National In-           1. Network analysis is a structural ap-
                                                                                                      stitutes of Health report “Toward Higher                 proach that focuses in part on patterns
                                                                                                      Levels of Analysis: Progress and Promise                 of linkages between actors;
                                                                                                      in Research on Social and Cultural Dimen-             2. it is grounded in empirical data;
                                                                                                      sions of Health” (110) lays out an ecologi-           3. it makes frequent use of mathematical
                                                                                                      cal and multilevel national research agenda,             and computational models; and
                                                                                                      and its recommendations include support for           4. it is highly graphical.
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                                      increased use of measurement at the “group,
                                                                                                      network, neighborhood, and community lev-
                                                                                                                                                         HISTORY AND DEVELOPMENT
                                                                                                      els” (p. 3). This recommendation recognizes
                                                                                                                                                         OF NETWORK ANALYSIS
                                                                                                      an important gap: Although ecological think-
                                                                                                      ing is part of the mainstream in the health        Network analysis has a long and complex his-
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                                      sciences (59), we lag behind in having a vari-     tory drawing on traditions in many different
                                                                                                      ety of ecological methods and tools that are       research disciplines. In some cases its develop-
                                                                                                      routinely used in studies of health (95). In       ment was stepwise, with new ideas building on
                                                                                                      public health, much of what we study is in-        existing work; other times concurrent devel-
                                                                                                      herently relational: disease transmission, dif-    opment was occurring in different fields. The
                                                                                                      fusion of innovations, coalitions, peer influ-      following brief overview highlights some of
                                                                                                      ence on risky behavior, etc. Network analysis      the major milestones in the development of
                                                                                                      is a research approach that is uniquely suited     social network analysis. For a more detailed
                                                                                                      to describing, exploring, and understanding        treatment of the history of network analysis,
                                                                                                      these types of structural and relational aspects   see Freeman (51).
                                                                                                      of health. This review outlines the history of         Eighteenth-century European math-
                                                                                                      network analysis, provides a brief overview        ematician Leonhard Euler used a visual
                                                                                                      of network methods, and shows where and            representation of a network of bridges and
                                                                                                      how network analysis has been used in public                                             ¨
                                                                                                                                                         rivers to solve the now famous Konigsberg
                                                                                                      health.                                            bridge problem (30). The problem asked
                                                                                                          A network consists of actors that represent    if it was possible to walk around the town
                                                                                                      individuals, organizations, programs, or other           ¨
                                                                                                                                                         of Konigsberg, crossing each of its seven
                                                                                                      entities. As this review shows, a network can      bridges only once, and returning to the
                                                                                                      be four different things: a conceptual model,      point of origin. By portraying the bridges
                                                                                                      a description of an existing real-world struc-     and land as points with lines between them,
                                                                                                      ture or system, a mathematical model, or a         Euler determined that no such path existed
                                                                                                      simulation. We typically depict a network as       owing to the number of nodes and links.
                                                                                                      a set of actors connected by lines or arrows       In doing so, Euler invented graph theory,
                                                                                                      which show some relationship between               which provides one of the mathematical
                                                                                                      them. For example, Figure 1 shows tobacco          foundations for network analysis. Figure 2
                                                                                                      control agencies in Oregon. The color and                                         ¨
                                                                                                                                                         shows a version of the Konigsberg map
                                                                                                      size of the nodes show the type of agency          and the network developed to explore the
                                                                                                      and its role within the network; the links         problem.
                                                                                                      between nodes represent contact between                Throughout the 1800s and early 1900s
                                                                                                      agencies.                                          social scientists posed questions about social


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                                                                                         ties and developed theories and terminol-             From the mid 1950s to the early 1970s,
                                                                                         ogy to describe social connections and social     fields such as sociology, anthropology, and
                                                                                         structure (51). Renowned sociologists such as     mathematics contributed conceptual, theo-
                                                                                         Comte and Simmel are often credited with          retical, and methodological advances that
                                                                                         many of the early ideas providing a foundation    helped to solidify the foundation of modern
                                                                                         for social network analysis. Important contri-    social network analysis (11, 61, 144). One
                                                                                         butions were also made during this time by        of the landmark articles in Sociometry dur-
                                                                                         lesser-known social scientists such as ethnol-    ing this time was a study examining interper-
                                                                                         ogist Eilert Sundt, who studied the forma-        sonal communication among physicians and
                                                                                         tion of social circles among rurual Norwegian     the diffusion of new drugs by Coleman, Katz,
                                                                                         farmers (33).                                     and Menzel (39). Coleman, Katz, and Menzel
                                                                                             In 1929 a new idea about ties between peo-    found that the number and types of social con-
                                                                                         ple was proposed in a short story by Hun-         nections physicians had influenced their adop-
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                                                                                         garian writer Frigyes Karinthy. In the story, a   tion of a new drug with close professional ties
                                                                                         character asserted that he could link anyone in   facilitating the earliest adoptions.
                                                                                         the world to himself through at most five ac-          In 1959, mathematicians Paul Erdos and ˝
                                                                                         quaintances, proposing what may be the first       Alfr´ d R´ nyi proposed one of the first for-
                                                                                                                                                e     e
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         mention of the concept of six degrees of sepa-                                     ˝
                                                                                                                                           mal network models. The Erdos-R´ nyi model
                                                                                                                                                                                 e
                                                                                         ration (109). In Karinthy’s time this assertion   portrayed networks as completely random
                                                                                         became a popular game, and it remains a part      (9). Surprisingly they found with this model
                                                                                         of popular culture today. Recent appearances      that the larger the size of the network, the
                                                                                         of the concept are found on numerous Web          fewer connections between network nodes
                                                                                         sites and in John Guare’s play, Six Degrees of    were needed to have the network be com-
                                                                                         Separation. The concept of six degrees of sep-    pletely linked. In fact, according to this model,
                                                                                         aration was one of the first demonstrations        connecting all six billion people in the world
                                                                                         that a network approach could be used to dis-     would require each person to have only about
                                                                                         cover important characteristics of the natural    24 random acquaintances (30). This random
                                                                                         world.                                            graph model was an early successful attempt
                                                                                             In the 1920s educational psychologists        to provide an explanation for how actual net-
                                                                                         published a number of studies reporting on        works operate and paved the way for modern
                                                                                         characteristics of social ties such as influ-      mathematical network theory (109).
                                                                                         ence, interaction, and companionship (50).            In the early 1970s sociologist Mark
                                                                                         Although many important network ideas             Granovetter proposed a network model that
                                                                                         came from this early work, the studies are        accounted for some basic truths about human
                                                                                         often overshadowed by the major contribu-                                                 ˝
                                                                                                                                           social ties (58). Although the Erdos-R´ nyi  e
                                                                                         tion made in 1934 by psychiatrist Jacob L.        network explained why large networks can be
                                                                                         Moreno (100). Moreno developed a new way          connected with a small number of ties (i.e.,
                                                                                         of representing relationships on paper, called    the “small world” phenomenon), most indi-
                                                                                         a “sociogram.” A sociogram was a drawing          viduals are not likely to be randomly con-
                                                                                         with points representing people connected by      nected to 24 others around the world. It is
                                                                                         lines representing interpersonal relationships.   more reasonable to assume that people know
                                                                                         Moreno’s work established network analysis as     their neighbors, coworkers, and families. Gra-
                                                                                         a unique discipline, and his sociograms were      novetter posited that, in addition to strong ties
                                                                                         the first specific network analytic tool (141).     to families, neighbors, and coworkers, each
                                                                                         In 1937 Moreno founded the journal Sociome-       person has weak ties to people such as casual
                                                                                         try, which published many of the early studies    acquaintances and that these weak ties held
                                                                                         taking network approaches or developing net-      the network together. The acquaintances and
                                                                                         work methods.                                     friends of friends reached outside what might

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                                                                                                      otherwise be closed and segmented networks         journals focusing on network analysis ap-
                                                                                                      of strong ties, allowing a larger network to       peared (e.g., Social Networks), and interna-
                                                                                                      form (58).                                         tional conferences were established (i.e., the
                                                                                                          Granovetter’s work is important for sev-       annual Sunbelt Conference). One critical as-
                                                                                                      eral reasons. First, it helped develop a so-       pect of the success of social network analy-
                                                                                                      phisticated and realistic model of network         sis was the development and availability of
                                                                                                      structure (58). More importantly for its subse-    software packages, including UCINET (25)
                                                                                                      quent utility for public health, Granovetter’s     and Pajek (13). As network analysis grew and
                                                                                                      work was among the first applications of net-       was applied in various mathematical, biologi-
                                                                                                      work theory, which attempted to explain social     cal, behavioral, and organizational contexts, it
                                                                                                      structure and human behavior. Granovetter’s        became clear that it was not simply a new an-
                                                                                                      theory of weak ties arose out of a simple ques-    alytic tool, but a distinctive theoretical disci-
                                                                                                      tion: “How do people find jobs?” The surpris-       pline. In fact, network analysis can be seen as a
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                                      ing answer that people find jobs through ac-        type of “normal” science, using Kuhn’s termi-
                                                                                                      quaintances rather than through close friends      nology (65, 85). Network analysis, thus, pro-
                                                                                                      led to a deeper understanding of how knowl-        vides public health with a new way of framing
                                                                                                      edge and information can be efficiently passed      and answering important health questions. To
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                                      through large social networks.                     introduce some of the major differences be-
                                                                                                          In recent years mathematicians and physi-      tween network approaches and traditional re-
                                                                                                      cists have started examining the fundamental       search methodology, the next section contains
                                                                                                      properties of theoretical and real-world net-      an overview of network methods.
                                                                                                      works. Drawing on the work of social sci-
                                                                                                      entists in measuring network centralization
                                                                                                      (49, 126) physicists developed models such         A BRIEF OVERVIEW OF
                                                                                                      as the small-world model and the scale-free        NETWORK ANALYSIS
                                                                                                      model, which have been useful in describ-          METHODS
                                                                                                      ing very large networks (9, 143). In particu-      The inherently relational quality of network
                                                                                                      lar, scale-free networks have hubs, or a few       methods requires a shift in thinking when it
                                                                                                      nodes that have an unusually high number           comes to research methodology. Network ap-
                                                                                                      of links, whereas other nodes have a small         proaches focus on relationships between sub-
                                                                                                      and relatively consistent number of links. This    jects rather than relationships between sub-
                                                                                                      structure has since been identified in diverse      ject attributes (i.e., variables). Study design,
                                                                                                      networks such as sexual partners in the early      data collection, and data analysis incorporate
                                                                                                      stages of the AIDS epidemic, the national and      this relational perspective, requiring unique
                                                                                                      international network of airports and flights,      approaches to each.
                                                                                                      and networks of large businesses (9).
                                                                                                          Social network analysis rapidly developed
                                                                                                      as a distinct discipline in the decades follow-    Study Design and Data Collection
                                                                                                      ing the 1970s (51). Important contributions        Traditional study designs in public health typ-
                                                                                                      were made from an extremely wide variety           ically utilize attribute data at the individual
                                                                                                      of fields, including sociology, psychology, po-     level. For these types of designs, data can be
                                                                                                      litical science, anthropology, communication,      collected from individuals before the entire
                                                                                                      business, mathematics (especially graph the-       sample has been identified, recruited, or in-
                                                                                                      ory), statistics, computer science, and physics.   terviewed. Data collection in network stud-
                                                                                                      In 1977 the professional association for so-       ies works quite differently. For many network
                                                                                                      cial network analysis was founded: the Inter-      studies, the entire network must be identi-
                                                                                                      national Network for Social Network Analy-         fied before data collection starts. For example,
                                                                                                      sis (INSNA). Shortly thereafter professional       in a study of student friendships, students in

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                                                                                                 Table 1     Comparison of attribute data format (top) and network data format
                                                                                                 (bottom)
                                                                                                 Attribute data
                                                                                                 ID            Age        Gender   Educ.     # Partners         Diagnosed
                                                                                                 1             25           M      Low           7                  Y
                                                                                                 2             32           F      Low           3                  N
                                                                                                 3             33           F      High          4                  N
                                                                                                 4             34           M      Med.          4                  Y
                                                                                                 5             40           F      Med.          2                  N
                                                                                                 6             37           M      High          5                  N
                                                                                                 Network (friendship) data
                                                                                                 ID            Bob        Karen    Nancy        Peter            Roberta           Scott
                                                                                                 Bob            0           0        0            1                0                 1
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                                                                                                 Karen          0           0        1            1                1                 0
                                                                                                 Nancy          0           1        0            1                1                 1
                                                                                                 Peter          1           1        1            0                0                 1
                                                                                                 Roberta        0           1        1            0                0                 1
                                                                                                 Scott          1           0        1            1                1                 0
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         particular classrooms would be identified be-       driven sampling (43, 120). This type of sam-
                                                                                         fore starting to collect network data. Then,       pling falls into the larger category of link-
                                                                                         every student in a classroom would be asked        tracing designs (128). Here, the researcher
                                                                                         about every other student to ascertain the re-     starts with a small number of network mem-
                                                                                         lationships. Table 1 shows how the resulting       bers and asks them who else should be in-
                                                                                         data could be organized, comparing data from       cluded in the network. These new network
                                                                                         a traditional individual-level study design to     members are then approached and are in turn
                                                                                         relational data obtained in a network study. In    asked to nominate network members. Typi-
                                                                                         individual attribute studies, the data are orga-   cally, after a small number of waves network
                                                                                         nized in an N-by-k rectangular matrix, with        members start nominating people who have
                                                                                         N subjects measured on k attributes. In net-       already been nominated. For more informa-
                                                                                         work analyses, data are typically organized in     tion about network study design see the 2004
                                                                                         an N-by-N square matrix. Thus, the data en-        text by Morris (101) and the 1992 article by
                                                                                         tries represent a relationship between a pair      Doreian & Woodard (43).
                                                                                         of actors (in this case, a friendship relation).
                                                                                             This type of network data collection is
                                                                                         sometimes referred to as complete or bounded       Data Analysis
                                                                                         because it is based on prior identification of      Although many ways exist to analyze net-
                                                                                         all network members. In many cases, net-           work data, three broad approaches to analysis
                                                                                         work identification is straightforward, espe-       are generally used. First, network visualiza-
                                                                                         cially when boundaries are clear. For exam-        tion allows researchers and audiences to view
                                                                                         ple, a network analysis of a substance abuse       various graphical depictions of networks. Sec-
                                                                                         referral network would identify all social ser-    ond, descriptive analyses of network proper-
                                                                                         vice agencies in a particular county that pro-     ties can reveal important details concerning
                                                                                         vide or receive referrals for substance abuse      the (a) position of network actors, (b) prop-
                                                                                         services. However, in many cases, network          erties of network subgroups (called a sub-
                                                                                         identification may not have clearly defined          graph), or (c) characteristics of a complete net-
                                                                                         boundaries. One useful network sampling ap-        work (Table 2 provides definitions and terms
                                                                                         proach is snowball sampling or respondent-         used at each level). Third, recent work in

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                                                                                         Table 2      Network levels of analysis with descriptions and network measures
                                                                                         Level            Definition and purpose                                          Standard network measures
                                                                                         Individual      A single actor or node         Degree             Connectivity of a given actor or node given by the
                                                                                                                                                            number of lines that are incident (connected) to the node
                                                                                                         Identification of the           Centrality         Importance or prominence of a given actor or node
                                                                                                          position or location and                         Following are several types of centrality:
                                                                                                          characteristics of an actor                       Betweenness: extent to which an actor lies between two
                                                                                                          within a network                                   nodes that would not otherwise be connected
                                                                                                                                                            Closeness: how close an actor is to all other actors on the
                                                                                                                                                             basis of distance between nodes
                                                                                                                                                            Degree: extent to which an actor is connected to others;
                                                                                                                                                             the simplest of the centrality measures
                                                                                                                                                            Prestige: specifically for directed networks; extent to
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                                                                                                                                                             which other members choose a given actor or node
                                                                                                                                        Structural         Extent to which actors play similar roles within a network
                                                                                                                                         equivalence        by having the same patterns of connections to other
                                                                                                                                                            actors
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         Subgraph        A subset of the graph          Dyad               A pair of actors and the possible tie between them
                                                                                                          based on certain nodes or     Triad              Three actors and the ties between them
                                                                                                          links
                                                                                                         Examination of                 k-core             All nodes in a network with degree ≥k
                                                                                                          characteristics of a group    Clique             Three or more actors connected by all possible
                                                                                                                                                            connections
                                                                                         Network         The entire system of           Density            Ratio of observed ties to possible ties
                                                                                                          nodes and links               Diameter           Longest of all geodesics (shortest path between two
                                                                                                                                                            nodes)
                                                                                                         Description or inference       Centralization     Extent to which the graph shows a hierarchical or
                                                                                                          based on the structure of                         centralized structure
                                                                                                          the entire network



                                                                                                                  stochastic and longitudinal network methods       two ways of displaying the same tobacco con-
                                                                                                                  allows investigators to build and test inferen-   trol network. On top is a ring network, where
                                                                                                                  tial and longitudinal network models.             all the nodes are arranged in an oval. This
                                                                                                                                                                    configuration is limited in that it becomes
                                                                                                                  Network visualization. Network visualiza-         hard to determine which nodes are more (or
                                                                                                                  tion consists of presenting network informa-      less) connected to others. In comparison, the
                                                                                                                  tion in graphic format and is a major part of     bottom figure uses an energy or spring em-
                                                                                                                  social network analysis. Figure 3, for exam-      bedding algorithm to position more central
                                                                                                                  ple, depicts the friendship network based on      nodes (those with more connections) toward
                                                                                                                  data from Table 2. Graphic representation al-     the center of the network (54), making it eas-
                                                                                                                  lows researchers to ask and answer questions      ier to see the structure. Modern visualization
                                                                                                                  about the network that might not be statis-       techniques have been developed to display
                                                                                                                  tically obvious. Modern network software in-      large and complicated networks in two- and
                                                                                                                  corporates layout and presentation algorithms     three-dimensional space (68).
                                                                                                                  that facilitate efficient and accurate interpre-
                                                                                                                  tation of network graphs. This is important       Network description. As Table 2 suggests,
                                                                                                                  because networks can be displayed in a va-        network description can focus on the role of
                                                                                                                  riety of ways. For example, Figure 4 shows        individual actors in the network, identification

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                                                                                                                                       Peter

                                                                                               Bob

                                                                                                                                                                                                       Figure 3
                                                                                                                                                                                  Karen                This network
                                                                                                                                                                                                       graphic depicts the
                                                                                                                                                                                                       friendship ties
                                                                                                                                                                                                       between six
                                                                                                                                                      Nancy                                            individuals. This was
                                                                                                                                                                                                       developed by the
                                                                                                               Scott                                                                                   authors for the
                                                                                                                                                                                                       purpose of
                                                                                                                                                                                                       demonstrating how
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                                                                                                                                                                                                       network data is
                                                                                                                                                                                                       visualized. The data
                                                                                                                                                                                                       underlying the
                                                                                                                                                                                                       network can be
                                                                                                                                                           Roberta                                     found in Table 2.
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         and interpretation of subgroups (called a sub-        Subgraph analysis consists of identifying
                                                                                         graph), and analysis of overall network struc-    and analyzing a subset of links and nodes from
                                                                                         ture. For a more formal and complete treat-       a network. This approach is used to under-
                                                                                         ment of network methods, see the Wasserman        stand cohesion in groups and to identify char-
                                                                                         & Faust text (141). Analysis at the individ-      acteristics of dyads, triads, and other subsets
                                                                                         ual level typically consists of identifying the   (Table 2). For example, in an article about
                                                                                         position or location of an actor within a net-    risk potential for HIV infection (53) Fried-
                                                                                         work. Traditionally, researchers have paid at-    man et al. used subgraph analysis to find all the
                                                                                         tention particularly to actors who play central   components comprised of individuals in the
                                                                                         roles, for example, those who are chosen more     network that had two or more drug-injecting
                                                                                         frequently by other network members (high         or sexual links. They determined that this sub-
                                                                                         prestige) or who act as brokers in communica-     set of individuals was an appropriate target
                                                                                         tion or transmission networks (high between-      for HIV prevention efforts because they were
                                                                                         ness). For example, in a study of adolescent      more likely to be HIV positive or engage in
                                                                                         smoking, Ennett & Bauman (45) identified           high-risk behaviors.
                                                                                         three positions in social networks associated         Finally, network description can focus
                                                                                         with transmission of health behaviors: isolate,   on the overall structure of the network.
                                                                                         bridge, and clique member. These positions        Network-level statistics provide insight into
                                                                                         were defined by the number and types of links      how connected a network is or how flat
                                                                                         individuals had to others in the network, and     or hierarchical the relationship structure is.
                                                                                         each position was associated with a different     Analyses of public health systems often re-
                                                                                         probability of adopting a particular health be-   port network-level results because they are
                                                                                         havior. Ennett & Bauman found that isolates,      typically examining collaboration in a group
                                                                                         or adolescents with few or no links to others,    of agencies (84, 115). For example, in an ar-
                                                                                         were more likely to be smokers than were ado-     ticle about a health policy network address-
                                                                                         lescents in bridge or clique positions. A later   ing diabetes along the U.S.-Mexican border
                                                                                         study determined that, among middle school        (115), Provan et al. compared the density of
                                                                                         students, popular students with many links to     a network of agencies for four different rela-
                                                                                         others were more likely to become smokers         tions: sharing information, sharing resources,
                                                                                         (139).                                            working together on projects, and sharing

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                                                                                                                    referrals. They found that the information-       Transmission Networks
                                                                                                                    sharing network had the highest density, sug-
                                                                                                                                                                      Analysis of transmission networks represents
                                                                                                                    gesting that information was passed between
                                                                                         STD: sexually                                                                a common use of network analysis in public
                                                                                         transmitted disease        agencies more frequently than were resources
                                                                                                                                                                      health. Transmission networks are social sys-
                                                                                                                    or referrals.
                                                                                                                                                                      tems that structure the flow of some tangi-
                                                                                                                                                                      ble element. Here the emphasis is on what
                                                                                                                    Stochastic and longitudinal networks.             flows between actors in a network. There
                                                                                                                    One limitation of the preceding methods           are two major types of transmission networks
                                                                                                                    is that they are fundamentally descriptive.       studied in public health: disease transmis-
                                                                                                                    Network data is, by definition, nonindepen-        sion networks and information transmission
                                                                                                                    dent, and thus traditional parametric mod-        networks.
                                                                                                                    els, that require independence of observa-
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                                                    tions cannot be applied. In the past decade,
                                                                                                                                                                      Disease transmission networks. Friedman
                                                                                                                    however, researchers have developed stochas-
                                                                                                                                                                      & Aral (52) defined disease transmission net-
                                                                                                                    tic network modeling methods, which can
                                                                                                                                                                      works as risk potential networks, which are
                                                                                                                    be used to test network hypotheses (142).
                                                                                                                                                                      networks of individuals connected by ties that
                                                                                                                    Also, new methods have been developed
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                                                                                                      can spread infection. As Eames & Keeling
                                                                                                                    that allow analysis of longitudinal network
                                                                                                                                                                      pointed out (44), “A wide range of com-
                                                                                                                    data (127). To date, only a handful of pub-
                                                                                                                                                                      municable human diseases can be consid-
                                                                                                                    lic health studies have utilized stochastic
                                                                                                                                                                      ered as spreading through a network of pos-
                                                                                                                    (102, 103) or longitudinal (111, 133, 134)
                                                                                                                                                                      sible transmission routes. The implied net-
                                                                                                                    methods.
                                                                                                                                                                      work structure is vital in determining disease
                                                                                                                                                                      dynamics. . .” (p. 13,330).
                                                                                                                                                                          These ties include behaviors such as nee-
                                                                                                                    THE USE OF NETWORK                                dle sharing or risky sexual activity, as well as
                                                                                                                    ANALYSIS IN PUBLIC HEALTH                         seemingly less risky connections such as liv-
                                                                                                                    Public health has long recognized the im-         ing in the same household or belonging to
                                                                                                                    portance of relational characteristics in un-     the same friendship group. In terms of risk
                                                                                                                    derstanding disease and health. The role of       potential, network analysis has been used pri-
                                                                                                                    close physical contact in communicable dis-       marily to look at the spread of HIV/AIDS,
                                                                                                                    ease outbreaks and the influence of peers on       other sexually transmitted diseases (STDs),
                                                                                                                    adolescent smoking and substance use are two      and other infectious diseases. Much of this
                                                                                                                    notable examples. However, although public        research has highlighted differences between
                                                                                                                    health has often adopted an ecological frame-     network approaches and traditional epidemi-
                                                                                                                    work that recognized the importance of re-        ological models of STDs and HIV.
                                                                                                                    lational information, only relatively recently        Traditional disease outbreak models ex-
                                                                                                                    have scholars utilized a more explicit network    amining person-to-person spread of infection
                                                                                                                    analytic approach. Our review suggests that       typically consist of the frequency of cases over
                                                                                                                    the use of network analysis in public health      time (78), whereas network models of trans-
                                                                                                                    falls into three broad categories: transmission   mission show relationships among individu-
                                                                                                                    networks, social networks, and organizational     als. The difference can be seen in Figure 6
                                                                                                                    networks (see Figure 5). This organization        with an epidemic curve showing the spread of
                                                                                                                    is not based on particular network analytic       syphilis on the left (34) and a network graph
                                                                                                                    methods or theory per se; rather, it reflects      modeling the spread of syphilis (in a differ-
                                                                                                                    how public health researchers have utilized       ent population) on the right (119). The epi-
                                                                                                                    network analytic tools to address public health   demiologic model is most useful for identi-
                                                                                                                    problems.                                         fying the course of an outbreak or epidemic,

                                                                                                               76   Luke   ·   Harris
ANRV305-PU28-05                                                                         ARI     6 March 2007   17:8




                                                                                         whereas the network model reveals the un-          of AIDS risk behaviors and HIV infection
                                                                                         derlying transmission structure of the out-        rates (41, 53). These studies, based on a pop-
                                                                                         break. The network model is useful particu-        ulation of 767 injecting drug users (IDU) in
                                                                                                                                                                                                        IDU: injection (or
                                                                                         larly for planning interventions for the disease   New York, reported that a higher percentage                 intravenous) drug
                                                                                         in question (147). These figures are included       of core and inner periphery members were                    user
                                                                                         to allow the reader to compare traditional         HIV positive. Core members were those con-
                                                                                         epidemiologic methods with network analytic        sidered “regular” members by others in the
                                                                                         methods.                                           network, whereas inner-periphery members
                                                                                             Network-like diagrams depicting disease        were those who had shared drugs with a core
                                                                                         transmission appeared in print as early as 1940    member in the past 30 days but were not in
                                                                                         (31). More recently, similar diagrams depict-      the core. In addition to having a higher rate
                                                                                         ing the early spread of HIV/AIDS were pre-         of HIV, these core and inner-periphery net-
                                                                                         sented as a tool for understanding and ad-         work members were involved in risk behav-
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                         dressing this emerging health problem. In          iors such as sharing syringes more often than
                                                                                         1984, just as the American public became           were network members in the outer periph-
                                                                                         aware of the AIDS epidemic, Auerbach and           ery. Another study of IDUs found that in-
                                                                                         colleagues published an article entitled “Clus-    dividuals were more likely to share needles
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         ter of Cases of the Acquired Immune De-            with strongly connected friends than with new
                                                                                         ficiency Syndrome” in the American Journal          friends or friends who were weakly connected
                                                                                         of Medicine (7). The article presented a dia-      (140). This factor reduced their short-term
                                                                                         gram of 40 AIDS patients in 10 cities linked       risk of HIV but not the long-term risk owing
                                                                                         by sexual contact. This depiction was among        to the high level of turnover in friendships
                                                                                         the first evidence that AIDS was an infectious      in this population. By examining the social
                                                                                         disease and was transmitted through sexual         networks of another population of IDUs, re-
                                                                                         contact. In 1985 Klovdahl took a network ap-       searchers also found that the larger and denser
                                                                                         proach to analyzing the data from the Auer-        a person’s drug network was, the more likely
                                                                                         bach et al. study (80). His conceptualization      he/she was to share needles (87). In general,
                                                                                         of disease transmission as a social network        the more close or strong ties an IDU has, the
                                                                                         allowed researchers the opportunity to con-        more likely he/she is to share needles and to
                                                                                         sider disease in a new way, which marked           be at risk for HIV (140).
                                                                                         a transition to wider use of network con-              In addition to individual network position
                                                                                         cepts and methods for studying infectious dis-     and composition, structural network prop-
                                                                                         eases. Since that time, numerous other stud-       erties have been associated with the epi-
                                                                                         ies have considered risk potential networks        demic stage or level of transmission of HIV
                                                                                         and HIV/AIDS transmission. These studies           within a population. The amount of assor-
                                                                                         have focused primarily on sexual and needle-       tative and disassortative mixing within the
                                                                                         sharing networks and identified risk factors as-    network and the presence of cyclic or den-
                                                                                         sociated with network characteristics (41, 53,     dritic structures are indicators of how HIV is
                                                                                         87, 104). In addition, characteristics of net-     spreading through the population (113, 114).
                                                                                         work structure have been associated with the       Assortative mixing occurs when people who
                                                                                         various stages of HIV epidemics (114).             have something in common are connected to
                                                                                             Through analysis of HIV/AIDS risk po-          each other. That is, a network where “birds of
                                                                                         tential networks, researchers have identified       a feather flock together” would be considered
                                                                                         a number of network-related risk factors for       assortative, whereas a network where “oppo-
                                                                                         HIV transmission, including network posi-          sites attract” would be considered disassorta-
                                                                                         tion and composition. In studies of street-        tive (102).
                                                                                         level drug markets, researchers found that             By simulating the spread of HIV through
                                                                                         network position was associated with levels        networks of sexual relationships, Morris &

                                                                                                                                            www.annualreviews.org • Network Analysis in Public Health   77
ANRV305-PU28-05                                                                            ARI   6 March 2007        17:8




                                                                                                                                               Cycles
Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org




                                                                                         Figure 7
                                                                                         A graph of the four
                                                                                         largest chlamydia
                                                                                         components in
                                                                                         Colorado Springs.
                by Dr. Douglas Luke on 05/26/07. For personal use only.




                                                                                         Adapted from
                                                                                         (113).

                                                                                                                 Kretzschmar (102) found that, compared with        area has focused on gaps in traditional epi-
                                                                                                                 random mixing, both assortative and disassor-      demiologic methods of contact tracing for
                                                                                                                 tative mixing regarding the number of sexual       STD prevention and control (6, 67, 82, 119).
                                                                                                                 partners increased the odds of a large epi-        The utility of network analysis for under-
                                                                                                                 demic once there had been an outbreak. Fur-        standing STDs was strikingly demonstrated
                                                                                                                 ther evidence to support this comes from two       to researchers and the public in 1998 when
                                                                                                                 studies that found that it was not just having     Rothenberg and colleagues (119) published
                                                                                                                 more partners that was a risk factor for becom-    an article on a syphilis outbreak in young
                                                                                                                 ing HIV positive; in fact, it was disassortative   teenage girls in an affluent Atlanta suburb. A
                                                                                                                 sexual partnerships between younger men and        network of 99 teenagers connected by sexual
                                                                                                                 older men that increased HIV risk (104, 122).      contact was identified when six girls, most un-
                                                                                                                     Mixing patterns are not the only factor in-    der the age of 16, were diagnosed with syphilis
                                                                                                                 fluencing HIV transmission networks. In a           (Figure 6b). Although the high level of sexual
                                                                                                                 study of network structure and STD, Potterat       activity among this group of young teenagers
                                                                                                                 and colleagues (113) identified cyclic struc-       appeared unique, a 2004 study (15) of the
                                                                                                                 tures, or closed loops, within a network as be-    population of students in a Midwestern high
                                                                                                                 ing loci of epidemics that are often present       school found a sexual and romantic relations
                                                                                                                 early in an epidemic. Conversely, dendritic,       network (Figure 8) that included 288 of the
                                                                                                                 or tree-like, structures appeared indicative of    832 students interviewed. Like the teenagers
                                                                                                                 the later phases of an epidemic where the rate     in Atlanta, these students were involved in
                                                                                                                 of new cases is decreasing (see Figure 7). In      a single large connected component, putting
                                                                                                                 a later study in the same community, Potterat      them at much greater risk for contracting an
                                                                                                                 and colleagues found a mixture of these two        STD.
                                                                                                                 structures in an HIV network. They suggested           Similar to findings in HIV/AIDS research,
                                                                                                                 that the hybrid network structure was associ-      the structure of an STD transmission network
                                                                                                                 ated with the low-to-moderate spread of HIV        may be different depending on the stage of
                                                                                                                 observed in the community (114).                   STD epidemic and the likelihood of assorta-
                                                                                                                     STDs have been another focus of pub-           tive or disassortative mixing in various pop-
                                                                                                                 lic health network research. Research in this      ulations (89, 113). Laumann and colleagues

                                                                                                           78    Luke   ·   Harris
Network analysis in public health (2)
Network analysis in public health (2)
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Network analysis in public health (2)

  • 1. ANRV305-PU28-05 ARI 6 March 2007 17:8 Network Analysis in Public Health: History, Methods, and Applications Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org Douglas A. Luke and Jenine K. Harris Department of Community Health, School of Public Health, Saint Louis University, St. Louis, Missouri 63104; email: dluke@slu.edu by Dr. Douglas Luke on 05/26/07. For personal use only. Annu. Rev. Public Health 2007. 28:69–93 Key Words The Annual Review of Public Health is online at social networks, disease transmission, diffusion of innovations, http://publhealth.annualreviews.org social support, social capital This article’s doi: 10.1146/annurev.publhealth.28.021406.144132 Abstract Copyright c 2007 by Annual Reviews. Network analysis is an approach to research that is uniquely suited All rights reserved to describing, exploring, and understanding structural and relational 0163-7525/07/0421-0069$20.00 aspects of health. It is both a methodological tool and a theoretical First published online as a Review in Advance on paradigm that allows us to pose and answer important ecological January 12, 2007 questions in public health. In this review we trace the history of network analysis, provide a methodological overview of network techniques, and discuss where and how network analysis has been used in public health. We show how network analysis has its roots in mathematics, statistics, sociology, anthropology, psychology, biol- ogy, physics, and computer science. In public health, network anal- ysis has been used to study primarily disease transmission, especially for HIV/AIDS and other sexually transmitted diseases; information transmission, particularly for diffusion of innovations; the role of social support and social capital; the influence of personal and social networks on health behavior; and the interorganizational structure of health systems. We conclude with future directions for network analysis in public health. 69
  • 2. ANRV305-PU28-05 ARI 6 March 2007 17:8 INTRODUCTION Network analysis, then, is the field that concerns itself with relational data and re- Over the past several decades researchers search questions. More specifically, the net- have placed increasing emphasis on using eco- work paradigm has four important features logical models and methods in the health (51): and social sciences in general, and public health in particular. The 2001 National In- 1. Network analysis is a structural ap- stitutes of Health report “Toward Higher proach that focuses in part on patterns Levels of Analysis: Progress and Promise of linkages between actors; in Research on Social and Cultural Dimen- 2. it is grounded in empirical data; sions of Health” (110) lays out an ecologi- 3. it makes frequent use of mathematical cal and multilevel national research agenda, and computational models; and and its recommendations include support for 4. it is highly graphical. Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org increased use of measurement at the “group, network, neighborhood, and community lev- HISTORY AND DEVELOPMENT els” (p. 3). This recommendation recognizes OF NETWORK ANALYSIS an important gap: Although ecological think- ing is part of the mainstream in the health Network analysis has a long and complex his- by Dr. Douglas Luke on 05/26/07. For personal use only. sciences (59), we lag behind in having a vari- tory drawing on traditions in many different ety of ecological methods and tools that are research disciplines. In some cases its develop- routinely used in studies of health (95). In ment was stepwise, with new ideas building on public health, much of what we study is in- existing work; other times concurrent devel- herently relational: disease transmission, dif- opment was occurring in different fields. The fusion of innovations, coalitions, peer influ- following brief overview highlights some of ence on risky behavior, etc. Network analysis the major milestones in the development of is a research approach that is uniquely suited social network analysis. For a more detailed to describing, exploring, and understanding treatment of the history of network analysis, these types of structural and relational aspects see Freeman (51). of health. This review outlines the history of Eighteenth-century European math- network analysis, provides a brief overview ematician Leonhard Euler used a visual of network methods, and shows where and representation of a network of bridges and how network analysis has been used in public ¨ rivers to solve the now famous Konigsberg health. bridge problem (30). The problem asked A network consists of actors that represent if it was possible to walk around the town individuals, organizations, programs, or other ¨ of Konigsberg, crossing each of its seven entities. As this review shows, a network can bridges only once, and returning to the be four different things: a conceptual model, point of origin. By portraying the bridges a description of an existing real-world struc- and land as points with lines between them, ture or system, a mathematical model, or a Euler determined that no such path existed simulation. We typically depict a network as owing to the number of nodes and links. a set of actors connected by lines or arrows In doing so, Euler invented graph theory, which show some relationship between which provides one of the mathematical them. For example, Figure 1 shows tobacco foundations for network analysis. Figure 2 control agencies in Oregon. The color and ¨ shows a version of the Konigsberg map size of the nodes show the type of agency and the network developed to explore the and its role within the network; the links problem. between nodes represent contact between Throughout the 1800s and early 1900s agencies. social scientists posed questions about social 70 Luke · Harris
  • 3. ANRV305-PU28-05 ARI 6 March 2007 17:8 ties and developed theories and terminol- From the mid 1950s to the early 1970s, ogy to describe social connections and social fields such as sociology, anthropology, and structure (51). Renowned sociologists such as mathematics contributed conceptual, theo- Comte and Simmel are often credited with retical, and methodological advances that many of the early ideas providing a foundation helped to solidify the foundation of modern for social network analysis. Important contri- social network analysis (11, 61, 144). One butions were also made during this time by of the landmark articles in Sociometry dur- lesser-known social scientists such as ethnol- ing this time was a study examining interper- ogist Eilert Sundt, who studied the forma- sonal communication among physicians and tion of social circles among rurual Norwegian the diffusion of new drugs by Coleman, Katz, farmers (33). and Menzel (39). Coleman, Katz, and Menzel In 1929 a new idea about ties between peo- found that the number and types of social con- ple was proposed in a short story by Hun- nections physicians had influenced their adop- Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org garian writer Frigyes Karinthy. In the story, a tion of a new drug with close professional ties character asserted that he could link anyone in facilitating the earliest adoptions. the world to himself through at most five ac- In 1959, mathematicians Paul Erdos and ˝ quaintances, proposing what may be the first Alfr´ d R´ nyi proposed one of the first for- e e by Dr. Douglas Luke on 05/26/07. For personal use only. mention of the concept of six degrees of sepa- ˝ mal network models. The Erdos-R´ nyi model e ration (109). In Karinthy’s time this assertion portrayed networks as completely random became a popular game, and it remains a part (9). Surprisingly they found with this model of popular culture today. Recent appearances that the larger the size of the network, the of the concept are found on numerous Web fewer connections between network nodes sites and in John Guare’s play, Six Degrees of were needed to have the network be com- Separation. The concept of six degrees of sep- pletely linked. In fact, according to this model, aration was one of the first demonstrations connecting all six billion people in the world that a network approach could be used to dis- would require each person to have only about cover important characteristics of the natural 24 random acquaintances (30). This random world. graph model was an early successful attempt In the 1920s educational psychologists to provide an explanation for how actual net- published a number of studies reporting on works operate and paved the way for modern characteristics of social ties such as influ- mathematical network theory (109). ence, interaction, and companionship (50). In the early 1970s sociologist Mark Although many important network ideas Granovetter proposed a network model that came from this early work, the studies are accounted for some basic truths about human often overshadowed by the major contribu- ˝ social ties (58). Although the Erdos-R´ nyi e tion made in 1934 by psychiatrist Jacob L. network explained why large networks can be Moreno (100). Moreno developed a new way connected with a small number of ties (i.e., of representing relationships on paper, called the “small world” phenomenon), most indi- a “sociogram.” A sociogram was a drawing viduals are not likely to be randomly con- with points representing people connected by nected to 24 others around the world. It is lines representing interpersonal relationships. more reasonable to assume that people know Moreno’s work established network analysis as their neighbors, coworkers, and families. Gra- a unique discipline, and his sociograms were novetter posited that, in addition to strong ties the first specific network analytic tool (141). to families, neighbors, and coworkers, each In 1937 Moreno founded the journal Sociome- person has weak ties to people such as casual try, which published many of the early studies acquaintances and that these weak ties held taking network approaches or developing net- the network together. The acquaintances and work methods. friends of friends reached outside what might www.annualreviews.org • Network Analysis in Public Health 71
  • 4. ANRV305-PU28-05 ARI 6 March 2007 17:8 otherwise be closed and segmented networks journals focusing on network analysis ap- of strong ties, allowing a larger network to peared (e.g., Social Networks), and interna- form (58). tional conferences were established (i.e., the Granovetter’s work is important for sev- annual Sunbelt Conference). One critical as- eral reasons. First, it helped develop a so- pect of the success of social network analy- phisticated and realistic model of network sis was the development and availability of structure (58). More importantly for its subse- software packages, including UCINET (25) quent utility for public health, Granovetter’s and Pajek (13). As network analysis grew and work was among the first applications of net- was applied in various mathematical, biologi- work theory, which attempted to explain social cal, behavioral, and organizational contexts, it structure and human behavior. Granovetter’s became clear that it was not simply a new an- theory of weak ties arose out of a simple ques- alytic tool, but a distinctive theoretical disci- tion: “How do people find jobs?” The surpris- pline. In fact, network analysis can be seen as a Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org ing answer that people find jobs through ac- type of “normal” science, using Kuhn’s termi- quaintances rather than through close friends nology (65, 85). Network analysis, thus, pro- led to a deeper understanding of how knowl- vides public health with a new way of framing edge and information can be efficiently passed and answering important health questions. To by Dr. Douglas Luke on 05/26/07. For personal use only. through large social networks. introduce some of the major differences be- In recent years mathematicians and physi- tween network approaches and traditional re- cists have started examining the fundamental search methodology, the next section contains properties of theoretical and real-world net- an overview of network methods. works. Drawing on the work of social sci- entists in measuring network centralization (49, 126) physicists developed models such A BRIEF OVERVIEW OF as the small-world model and the scale-free NETWORK ANALYSIS model, which have been useful in describ- METHODS ing very large networks (9, 143). In particu- The inherently relational quality of network lar, scale-free networks have hubs, or a few methods requires a shift in thinking when it nodes that have an unusually high number comes to research methodology. Network ap- of links, whereas other nodes have a small proaches focus on relationships between sub- and relatively consistent number of links. This jects rather than relationships between sub- structure has since been identified in diverse ject attributes (i.e., variables). Study design, networks such as sexual partners in the early data collection, and data analysis incorporate stages of the AIDS epidemic, the national and this relational perspective, requiring unique international network of airports and flights, approaches to each. and networks of large businesses (9). Social network analysis rapidly developed as a distinct discipline in the decades follow- Study Design and Data Collection ing the 1970s (51). Important contributions Traditional study designs in public health typ- were made from an extremely wide variety ically utilize attribute data at the individual of fields, including sociology, psychology, po- level. For these types of designs, data can be litical science, anthropology, communication, collected from individuals before the entire business, mathematics (especially graph the- sample has been identified, recruited, or in- ory), statistics, computer science, and physics. terviewed. Data collection in network stud- In 1977 the professional association for so- ies works quite differently. For many network cial network analysis was founded: the Inter- studies, the entire network must be identi- national Network for Social Network Analy- fied before data collection starts. For example, sis (INSNA). Shortly thereafter professional in a study of student friendships, students in 72 Luke · Harris
  • 5. ANRV305-PU28-05 ARI 6 March 2007 17:8 Table 1 Comparison of attribute data format (top) and network data format (bottom) Attribute data ID Age Gender Educ. # Partners Diagnosed 1 25 M Low 7 Y 2 32 F Low 3 N 3 33 F High 4 N 4 34 M Med. 4 Y 5 40 F Med. 2 N 6 37 M High 5 N Network (friendship) data ID Bob Karen Nancy Peter Roberta Scott Bob 0 0 0 1 0 1 Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org Karen 0 0 1 1 1 0 Nancy 0 1 0 1 1 1 Peter 1 1 1 0 0 1 Roberta 0 1 1 0 0 1 Scott 1 0 1 1 1 0 by Dr. Douglas Luke on 05/26/07. For personal use only. particular classrooms would be identified be- driven sampling (43, 120). This type of sam- fore starting to collect network data. Then, pling falls into the larger category of link- every student in a classroom would be asked tracing designs (128). Here, the researcher about every other student to ascertain the re- starts with a small number of network mem- lationships. Table 1 shows how the resulting bers and asks them who else should be in- data could be organized, comparing data from cluded in the network. These new network a traditional individual-level study design to members are then approached and are in turn relational data obtained in a network study. In asked to nominate network members. Typi- individual attribute studies, the data are orga- cally, after a small number of waves network nized in an N-by-k rectangular matrix, with members start nominating people who have N subjects measured on k attributes. In net- already been nominated. For more informa- work analyses, data are typically organized in tion about network study design see the 2004 an N-by-N square matrix. Thus, the data en- text by Morris (101) and the 1992 article by tries represent a relationship between a pair Doreian & Woodard (43). of actors (in this case, a friendship relation). This type of network data collection is sometimes referred to as complete or bounded Data Analysis because it is based on prior identification of Although many ways exist to analyze net- all network members. In many cases, net- work data, three broad approaches to analysis work identification is straightforward, espe- are generally used. First, network visualiza- cially when boundaries are clear. For exam- tion allows researchers and audiences to view ple, a network analysis of a substance abuse various graphical depictions of networks. Sec- referral network would identify all social ser- ond, descriptive analyses of network proper- vice agencies in a particular county that pro- ties can reveal important details concerning vide or receive referrals for substance abuse the (a) position of network actors, (b) prop- services. However, in many cases, network erties of network subgroups (called a sub- identification may not have clearly defined graph), or (c) characteristics of a complete net- boundaries. One useful network sampling ap- work (Table 2 provides definitions and terms proach is snowball sampling or respondent- used at each level). Third, recent work in www.annualreviews.org • Network Analysis in Public Health 73
  • 6. ANRV305-PU28-05 ARI 6 March 2007 17:8 Table 2 Network levels of analysis with descriptions and network measures Level Definition and purpose Standard network measures Individual A single actor or node Degree Connectivity of a given actor or node given by the number of lines that are incident (connected) to the node Identification of the Centrality Importance or prominence of a given actor or node position or location and Following are several types of centrality: characteristics of an actor Betweenness: extent to which an actor lies between two within a network nodes that would not otherwise be connected Closeness: how close an actor is to all other actors on the basis of distance between nodes Degree: extent to which an actor is connected to others; the simplest of the centrality measures Prestige: specifically for directed networks; extent to Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org which other members choose a given actor or node Structural Extent to which actors play similar roles within a network equivalence by having the same patterns of connections to other actors by Dr. Douglas Luke on 05/26/07. For personal use only. Subgraph A subset of the graph Dyad A pair of actors and the possible tie between them based on certain nodes or Triad Three actors and the ties between them links Examination of k-core All nodes in a network with degree ≥k characteristics of a group Clique Three or more actors connected by all possible connections Network The entire system of Density Ratio of observed ties to possible ties nodes and links Diameter Longest of all geodesics (shortest path between two nodes) Description or inference Centralization Extent to which the graph shows a hierarchical or based on the structure of centralized structure the entire network stochastic and longitudinal network methods two ways of displaying the same tobacco con- allows investigators to build and test inferen- trol network. On top is a ring network, where tial and longitudinal network models. all the nodes are arranged in an oval. This configuration is limited in that it becomes Network visualization. Network visualiza- hard to determine which nodes are more (or tion consists of presenting network informa- less) connected to others. In comparison, the tion in graphic format and is a major part of bottom figure uses an energy or spring em- social network analysis. Figure 3, for exam- bedding algorithm to position more central ple, depicts the friendship network based on nodes (those with more connections) toward data from Table 2. Graphic representation al- the center of the network (54), making it eas- lows researchers to ask and answer questions ier to see the structure. Modern visualization about the network that might not be statis- techniques have been developed to display tically obvious. Modern network software in- large and complicated networks in two- and corporates layout and presentation algorithms three-dimensional space (68). that facilitate efficient and accurate interpre- tation of network graphs. This is important Network description. As Table 2 suggests, because networks can be displayed in a va- network description can focus on the role of riety of ways. For example, Figure 4 shows individual actors in the network, identification 74 Luke · Harris
  • 7. ANRV305-PU28-05 ARI 6 March 2007 17:8 Peter Bob Figure 3 Karen This network graphic depicts the friendship ties between six Nancy individuals. This was developed by the Scott authors for the purpose of demonstrating how Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org network data is visualized. The data underlying the network can be Roberta found in Table 2. by Dr. Douglas Luke on 05/26/07. For personal use only. and interpretation of subgroups (called a sub- Subgraph analysis consists of identifying graph), and analysis of overall network struc- and analyzing a subset of links and nodes from ture. For a more formal and complete treat- a network. This approach is used to under- ment of network methods, see the Wasserman stand cohesion in groups and to identify char- & Faust text (141). Analysis at the individ- acteristics of dyads, triads, and other subsets ual level typically consists of identifying the (Table 2). For example, in an article about position or location of an actor within a net- risk potential for HIV infection (53) Fried- work. Traditionally, researchers have paid at- man et al. used subgraph analysis to find all the tention particularly to actors who play central components comprised of individuals in the roles, for example, those who are chosen more network that had two or more drug-injecting frequently by other network members (high or sexual links. They determined that this sub- prestige) or who act as brokers in communica- set of individuals was an appropriate target tion or transmission networks (high between- for HIV prevention efforts because they were ness). For example, in a study of adolescent more likely to be HIV positive or engage in smoking, Ennett & Bauman (45) identified high-risk behaviors. three positions in social networks associated Finally, network description can focus with transmission of health behaviors: isolate, on the overall structure of the network. bridge, and clique member. These positions Network-level statistics provide insight into were defined by the number and types of links how connected a network is or how flat individuals had to others in the network, and or hierarchical the relationship structure is. each position was associated with a different Analyses of public health systems often re- probability of adopting a particular health be- port network-level results because they are havior. Ennett & Bauman found that isolates, typically examining collaboration in a group or adolescents with few or no links to others, of agencies (84, 115). For example, in an ar- were more likely to be smokers than were ado- ticle about a health policy network address- lescents in bridge or clique positions. A later ing diabetes along the U.S.-Mexican border study determined that, among middle school (115), Provan et al. compared the density of students, popular students with many links to a network of agencies for four different rela- others were more likely to become smokers tions: sharing information, sharing resources, (139). working together on projects, and sharing www.annualreviews.org • Network Analysis in Public Health 75
  • 8. ANRV305-PU28-05 ARI 6 March 2007 17:8 referrals. They found that the information- Transmission Networks sharing network had the highest density, sug- Analysis of transmission networks represents gesting that information was passed between STD: sexually a common use of network analysis in public transmitted disease agencies more frequently than were resources health. Transmission networks are social sys- or referrals. tems that structure the flow of some tangi- ble element. Here the emphasis is on what Stochastic and longitudinal networks. flows between actors in a network. There One limitation of the preceding methods are two major types of transmission networks is that they are fundamentally descriptive. studied in public health: disease transmis- Network data is, by definition, nonindepen- sion networks and information transmission dent, and thus traditional parametric mod- networks. els, that require independence of observa- Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org tions cannot be applied. In the past decade, Disease transmission networks. Friedman however, researchers have developed stochas- & Aral (52) defined disease transmission net- tic network modeling methods, which can works as risk potential networks, which are be used to test network hypotheses (142). networks of individuals connected by ties that Also, new methods have been developed by Dr. Douglas Luke on 05/26/07. For personal use only. can spread infection. As Eames & Keeling that allow analysis of longitudinal network pointed out (44), “A wide range of com- data (127). To date, only a handful of pub- municable human diseases can be consid- lic health studies have utilized stochastic ered as spreading through a network of pos- (102, 103) or longitudinal (111, 133, 134) sible transmission routes. The implied net- methods. work structure is vital in determining disease dynamics. . .” (p. 13,330). These ties include behaviors such as nee- THE USE OF NETWORK dle sharing or risky sexual activity, as well as ANALYSIS IN PUBLIC HEALTH seemingly less risky connections such as liv- Public health has long recognized the im- ing in the same household or belonging to portance of relational characteristics in un- the same friendship group. In terms of risk derstanding disease and health. The role of potential, network analysis has been used pri- close physical contact in communicable dis- marily to look at the spread of HIV/AIDS, ease outbreaks and the influence of peers on other sexually transmitted diseases (STDs), adolescent smoking and substance use are two and other infectious diseases. Much of this notable examples. However, although public research has highlighted differences between health has often adopted an ecological frame- network approaches and traditional epidemi- work that recognized the importance of re- ological models of STDs and HIV. lational information, only relatively recently Traditional disease outbreak models ex- have scholars utilized a more explicit network amining person-to-person spread of infection analytic approach. Our review suggests that typically consist of the frequency of cases over the use of network analysis in public health time (78), whereas network models of trans- falls into three broad categories: transmission mission show relationships among individu- networks, social networks, and organizational als. The difference can be seen in Figure 6 networks (see Figure 5). This organization with an epidemic curve showing the spread of is not based on particular network analytic syphilis on the left (34) and a network graph methods or theory per se; rather, it reflects modeling the spread of syphilis (in a differ- how public health researchers have utilized ent population) on the right (119). The epi- network analytic tools to address public health demiologic model is most useful for identi- problems. fying the course of an outbreak or epidemic, 76 Luke · Harris
  • 9. ANRV305-PU28-05 ARI 6 March 2007 17:8 whereas the network model reveals the un- of AIDS risk behaviors and HIV infection derlying transmission structure of the out- rates (41, 53). These studies, based on a pop- break. The network model is useful particu- ulation of 767 injecting drug users (IDU) in IDU: injection (or larly for planning interventions for the disease New York, reported that a higher percentage intravenous) drug in question (147). These figures are included of core and inner periphery members were user to allow the reader to compare traditional HIV positive. Core members were those con- epidemiologic methods with network analytic sidered “regular” members by others in the methods. network, whereas inner-periphery members Network-like diagrams depicting disease were those who had shared drugs with a core transmission appeared in print as early as 1940 member in the past 30 days but were not in (31). More recently, similar diagrams depict- the core. In addition to having a higher rate ing the early spread of HIV/AIDS were pre- of HIV, these core and inner-periphery net- sented as a tool for understanding and ad- work members were involved in risk behav- Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org dressing this emerging health problem. In iors such as sharing syringes more often than 1984, just as the American public became were network members in the outer periph- aware of the AIDS epidemic, Auerbach and ery. Another study of IDUs found that in- colleagues published an article entitled “Clus- dividuals were more likely to share needles by Dr. Douglas Luke on 05/26/07. For personal use only. ter of Cases of the Acquired Immune De- with strongly connected friends than with new ficiency Syndrome” in the American Journal friends or friends who were weakly connected of Medicine (7). The article presented a dia- (140). This factor reduced their short-term gram of 40 AIDS patients in 10 cities linked risk of HIV but not the long-term risk owing by sexual contact. This depiction was among to the high level of turnover in friendships the first evidence that AIDS was an infectious in this population. By examining the social disease and was transmitted through sexual networks of another population of IDUs, re- contact. In 1985 Klovdahl took a network ap- searchers also found that the larger and denser proach to analyzing the data from the Auer- a person’s drug network was, the more likely bach et al. study (80). His conceptualization he/she was to share needles (87). In general, of disease transmission as a social network the more close or strong ties an IDU has, the allowed researchers the opportunity to con- more likely he/she is to share needles and to sider disease in a new way, which marked be at risk for HIV (140). a transition to wider use of network con- In addition to individual network position cepts and methods for studying infectious dis- and composition, structural network prop- eases. Since that time, numerous other stud- erties have been associated with the epi- ies have considered risk potential networks demic stage or level of transmission of HIV and HIV/AIDS transmission. These studies within a population. The amount of assor- have focused primarily on sexual and needle- tative and disassortative mixing within the sharing networks and identified risk factors as- network and the presence of cyclic or den- sociated with network characteristics (41, 53, dritic structures are indicators of how HIV is 87, 104). In addition, characteristics of net- spreading through the population (113, 114). work structure have been associated with the Assortative mixing occurs when people who various stages of HIV epidemics (114). have something in common are connected to Through analysis of HIV/AIDS risk po- each other. That is, a network where “birds of tential networks, researchers have identified a feather flock together” would be considered a number of network-related risk factors for assortative, whereas a network where “oppo- HIV transmission, including network posi- sites attract” would be considered disassorta- tion and composition. In studies of street- tive (102). level drug markets, researchers found that By simulating the spread of HIV through network position was associated with levels networks of sexual relationships, Morris & www.annualreviews.org • Network Analysis in Public Health 77
  • 10. ANRV305-PU28-05 ARI 6 March 2007 17:8 Cycles Annu. Rev. Public. Health. 2007.28:69-93. Downloaded from arjournals.annualreviews.org Figure 7 A graph of the four largest chlamydia components in Colorado Springs. by Dr. Douglas Luke on 05/26/07. For personal use only. Adapted from (113). Kretzschmar (102) found that, compared with area has focused on gaps in traditional epi- random mixing, both assortative and disassor- demiologic methods of contact tracing for tative mixing regarding the number of sexual STD prevention and control (6, 67, 82, 119). partners increased the odds of a large epi- The utility of network analysis for under- demic once there had been an outbreak. Fur- standing STDs was strikingly demonstrated ther evidence to support this comes from two to researchers and the public in 1998 when studies that found that it was not just having Rothenberg and colleagues (119) published more partners that was a risk factor for becom- an article on a syphilis outbreak in young ing HIV positive; in fact, it was disassortative teenage girls in an affluent Atlanta suburb. A sexual partnerships between younger men and network of 99 teenagers connected by sexual older men that increased HIV risk (104, 122). contact was identified when six girls, most un- Mixing patterns are not the only factor in- der the age of 16, were diagnosed with syphilis fluencing HIV transmission networks. In a (Figure 6b). Although the high level of sexual study of network structure and STD, Potterat activity among this group of young teenagers and colleagues (113) identified cyclic struc- appeared unique, a 2004 study (15) of the tures, or closed loops, within a network as be- population of students in a Midwestern high ing loci of epidemics that are often present school found a sexual and romantic relations early in an epidemic. Conversely, dendritic, network (Figure 8) that included 288 of the or tree-like, structures appeared indicative of 832 students interviewed. Like the teenagers the later phases of an epidemic where the rate in Atlanta, these students were involved in of new cases is decreasing (see Figure 7). In a single large connected component, putting a later study in the same community, Potterat them at much greater risk for contracting an and colleagues found a mixture of these two STD. structures in an HIV network. They suggested Similar to findings in HIV/AIDS research, that the hybrid network structure was associ- the structure of an STD transmission network ated with the low-to-moderate spread of HIV may be different depending on the stage of observed in the community (114). STD epidemic and the likelihood of assorta- STDs have been another focus of pub- tive or disassortative mixing in various pop- lic health network research. Research in this ulations (89, 113). Laumann and colleagues 78 Luke · Harris