Diese Präsentation wurde erfolgreich gemeldet.
Die SlideShare-Präsentation wird heruntergeladen. ×

Socialnetworkanalysis (Tin180 Com)

Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Anzeige
Wird geladen in …3
×

Hier ansehen

1 von 30 Anzeige

Weitere Verwandte Inhalte

Diashows für Sie (19)

Ähnlich wie Socialnetworkanalysis (Tin180 Com) (20)

Anzeige

Weitere von Tin180 VietNam (20)

Aktuellste (20)

Anzeige

Socialnetworkanalysis (Tin180 Com)

  1. 1. Social Network Analysis <ul><li>Social Network Introduction </li></ul><ul><li>Statistics and Probability Theory </li></ul><ul><li>Models of Social Network Generation </li></ul><ul><li>Networks in Biological System </li></ul>
  2. 2. Society Nodes : individuals Links : social relationship (family/work/friendship/etc.) S. Milgram (1967) Social networks: Many individuals with diverse social interactions between them. John Guare Six Degrees of Separation
  3. 3. Communication networks The Earth is developing an electronic nervous system, a network with diverse nodes and links are -computers -routers -satellites -phone lines -TV cables -EM waves Communication networks: Many non-identical components with diverse connections between them.
  4. 4. New York Times Complex systems Made of many non-identical elements connected by diverse interactions . NETWORK
  5. 5. “ Natural” Networks and Universality <ul><li>Consider many kinds of networks: </li></ul><ul><ul><li>social, technological, business, economic, content,… </li></ul></ul><ul><li>These networks tend to share certain informal properties: </li></ul><ul><ul><li>large scale; continual growth </li></ul></ul><ul><ul><li>distributed, organic growth: vertices “decide” who to link to </li></ul></ul><ul><ul><li>interaction restricted to links </li></ul></ul><ul><ul><li>mixture of local and long-distance connections </li></ul></ul><ul><ul><li>abstract notions of distance: geographical, content, social,… </li></ul></ul><ul><li>Do natural networks share more quantitative universals? </li></ul><ul><li>What would these “universals” be? </li></ul><ul><li>How can we make them precise and measure them? </li></ul><ul><li>How can we explain their universality? </li></ul><ul><li>This is the domain of social network theory </li></ul><ul><li>Sometimes also referred to as link analysis </li></ul>
  6. 6. Some Interesting Quantities <ul><li>Connected components : </li></ul><ul><ul><li>how many, and how large? </li></ul></ul><ul><li>Network diameter : </li></ul><ul><ul><li>maximum (worst-case) or average? </li></ul></ul><ul><ul><li>exclude infinite distances? (disconnected components) </li></ul></ul><ul><ul><li>the small-world phenomenon </li></ul></ul><ul><li>Clustering : </li></ul><ul><ul><li>to what extent that links tend to cluster “locally”? </li></ul></ul><ul><ul><li>what is the balance between local and long-distance connections? </li></ul></ul><ul><ul><li>what roles do the two types of links play? </li></ul></ul><ul><li>Degree distribution : </li></ul><ul><ul><li>what is the typical degree in the network? </li></ul></ul><ul><ul><li>what is the overall distribution? </li></ul></ul>
  7. 7. A “Canonical” Natural Network has… <ul><li>Few connected components: </li></ul><ul><ul><li>often only 1 or a small number, indep. of network size </li></ul></ul><ul><li>Small diameter: </li></ul><ul><ul><li>often a constant independent of network size (like 6) </li></ul></ul><ul><ul><li>or perhaps growing only logarithmically with network size or even shrink? </li></ul></ul><ul><ul><li>typically exclude infinite distances </li></ul></ul><ul><li>A high degree of clustering: </li></ul><ul><ul><li>considerably more so than for a random network </li></ul></ul><ul><ul><li>in tension with small diameter </li></ul></ul><ul><li>A heavy-tailed degree distribution: </li></ul><ul><ul><li>a small but reliable number of high-degree vertices </li></ul></ul><ul><ul><li>often of power law form </li></ul></ul>
  8. 8. Probabilistic Models of Networks <ul><li>All of the network generation models we will study are probabilistic or statistical in nature </li></ul><ul><li>They can generate networks of any size </li></ul><ul><li>They often have various parameters that can be set: </li></ul><ul><ul><li>size of network generated </li></ul></ul><ul><ul><li>average degree of a vertex </li></ul></ul><ul><ul><li>fraction of long-distance connections </li></ul></ul><ul><li>The models generate a distribution over networks </li></ul><ul><li>Statements are always statistical in nature: </li></ul><ul><ul><li>with high probability , diameter is small </li></ul></ul><ul><ul><li>on average , degree distribution has heavy tail </li></ul></ul><ul><li>Thus, we’re going to need some basic statistics and probability theory </li></ul>
  9. 9. Zipf’s Law <ul><li>Look at the frequency of English words: </li></ul><ul><ul><li>“ the” is the most common, followed by “of”, “to”, etc. </li></ul></ul><ul><ul><li>claim: frequency of the n-th most common ~ 1/n (power law, α = 1) </li></ul></ul><ul><li>General theme: </li></ul><ul><ul><li>rank events by their frequency of occurrence </li></ul></ul><ul><ul><li>resulting distribution often is a power law! </li></ul></ul><ul><li>Other examples: </li></ul><ul><ul><li>North America city sizes </li></ul></ul><ul><ul><li>personal income </li></ul></ul><ul><ul><li>file sizes </li></ul></ul><ul><ul><li>genus sizes (number of species) </li></ul></ul><ul><li>People seem to dither over exact form of these distributions (e.g. value of α ), but not heavy tails </li></ul>
  10. 10. Zipf’s Law Linear scales on both axes Logarithmic scales on both axes The same data plotted on linear and logarithmic scales. Both plots show a Zipf distribution with 300 datapoints
  11. 11. Social Network Analysis <ul><li>Social Network Introduction </li></ul><ul><li>Statistics and Probability Theory </li></ul><ul><li>Models of Social Network Generation </li></ul><ul><li>Networks in Biological System </li></ul><ul><li>Summary </li></ul>
  12. 12. Some Models of Network Generation <ul><li>Random graphs (Erdös-Rényi models): </li></ul><ul><ul><li>gives few components and small diameter </li></ul></ul><ul><ul><li>does not give high clustering and heavy-tailed degree distributions </li></ul></ul><ul><ul><li>is the mathematically most well-studied and understood model </li></ul></ul><ul><li>Watts-Strogatz models: </li></ul><ul><ul><li>give few components, small diameter and high clustering </li></ul></ul><ul><ul><li>does not give heavy-tailed degree distributions </li></ul></ul><ul><li>Scale-free Networks: </li></ul><ul><ul><li>gives few components, small diameter and heavy-tailed distribution </li></ul></ul><ul><ul><li>does not give high clustering </li></ul></ul><ul><li>Hierarchical networks: </li></ul><ul><ul><li>few components, small diameter, high clustering, heavy-tailed </li></ul></ul><ul><li>Affiliation networks: </li></ul><ul><ul><li>models group-actor formation </li></ul></ul>
  13. 13. The Clustering Coefficient of a Network <ul><li>Let nbr(u) denote the set of neighbors of u in a graph </li></ul><ul><ul><li>all vertices v such that the edge (u,v) is in the graph </li></ul></ul><ul><li>The clustering coefficient of u: </li></ul><ul><ul><li>let k = |nbr(u)| (i.e., number of neighbors of u) </li></ul></ul><ul><ul><li>choose(k,2): max possible # of edges between vertices in nbr(u) </li></ul></ul><ul><ul><li>c(u) = ( actual # of edges between vertices in nbr(u))/choose(k,2) </li></ul></ul><ul><ul><li>0 <= c(u) <= 1; measure of cliquishness of u’s neighborhood </li></ul></ul><ul><li>Clustering coefficient of a graph: </li></ul><ul><ul><li>average of c(u) over all vertices u </li></ul></ul>k = 4 choose(k,2) = 6 c(u) = 4/6 = 0.666…
  14. 14. Clustering : My friends will likely know each other! Probability to be connected C » p C = # of links between 1,2,…n neighbors n(n-1)/2 Networks are clustered [large C(p)] but have a small characteristic path length [small L(p)]. The Clustering Coefficient of a Network
  15. 15. Erdos-Renyi: Clustering Coefficient <ul><li>Generate a network G according to G(N,p) </li></ul><ul><li>Examine a “typical” vertex u in G </li></ul><ul><ul><li>choose u at random among all vertices in G </li></ul></ul><ul><ul><li>what do we expect c(u) to be? </li></ul></ul><ul><li>Answer: exactly p! </li></ul><ul><li>In G(N,m), expect c(u) to be 2m/N(N-1) </li></ul><ul><li>Both cases: c(u) entirely determined by overall density </li></ul><ul><li>Baseline for comparison with “more clustered” models </li></ul><ul><ul><li>Erdos-Renyi has no bias towards clustered or local edges </li></ul></ul>
  16. 16. Scale-free Networks <ul><li>The number of nodes (N) is not fixed </li></ul><ul><ul><li>Networks continuously expand by additional new nodes </li></ul></ul><ul><ul><ul><li>WWW: addition of new nodes </li></ul></ul></ul><ul><ul><ul><li>Citation: publication of new papers </li></ul></ul></ul><ul><li>The attachment is not uniform </li></ul><ul><ul><li>A node is linked with higher probability to a node that already has a large number of links </li></ul></ul><ul><ul><ul><li>WWW: new documents link to well known sites (CNN, Yahoo, Google) </li></ul></ul></ul><ul><ul><ul><li>Citation: Well cited papers are more likely to be cited again </li></ul></ul></ul>
  17. 17. Scale-Free Networks <ul><li>Start with (say) two vertices connected by an edge </li></ul><ul><li>For i = 3 to N: </li></ul><ul><ul><li>for each 1 <= j < i, d(j) = degree of vertex j so far </li></ul></ul><ul><ul><li>let Z = S d(j) (sum of all degrees so far) </li></ul></ul><ul><ul><li>add new vertex i with k edges back to {1, …, i-1}: </li></ul></ul><ul><ul><ul><li>i is connected back to j with probability d(j)/Z </li></ul></ul></ul><ul><li>Vertices j with high degree are likely to get more links! </li></ul><ul><li>“ Rich get richer” </li></ul><ul><li>Natural model for many processes: </li></ul><ul><ul><li>hyperlinks on the web </li></ul></ul><ul><ul><li>new business and social contacts </li></ul></ul><ul><ul><li>transportation networks </li></ul></ul><ul><li>Generates a power law distribution of degrees </li></ul><ul><ul><li>exponent depends on value of k </li></ul></ul>
  18. 18. <ul><li>Preferential attachment explains </li></ul><ul><ul><li>heavy-tailed degree distributions </li></ul></ul><ul><ul><li>small diameter (~log(N), via “hubs”) </li></ul></ul><ul><li>Will not generate high clustering coefficient </li></ul><ul><ul><li>no bias towards local connectivity, but towards hubs </li></ul></ul>Scale-Free Networks
  19. 19. Social Network Analysis <ul><li>Social Network Introduction </li></ul><ul><li>Statistics and Probability Theory </li></ul><ul><li>Models of Social Network Generation </li></ul><ul><li>Networks in Biological System </li></ul><ul><li>Mining on Social Network </li></ul><ul><li>Summary </li></ul>
  20. 20. Bio-Map protein-gene interactions protein-protein interactions PROTEOME GENOME Citrate Cycle METABOLISM Bio-chemical reactions
  21. 21. Citrate Cycle METABOLISM Bio-chemical reactions Metabolic Network
  22. 22. Boehring-Mennheim
  23. 23. Metab-movie Nodes : chemicals (substrates) Links : bio-chemical reactions Metabolic Network
  24. 24. Meta-P(k) Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, 407 651 (2000) Archaea Bacteria Eukaryotes Metabolic Network
  25. 25. Bio-Map protein-gene interactions protein-protein interactions PROTEOME GENOME Citrate Cycle METABOLISM Bio-chemical reactions
  26. 26. Protein Network protein-protein interactions PROTEOME
  27. 27. Prot Interaction map Nodes : proteins Links : physical interactions (binding) P. Uetz, et al. Nature 403 , 623-7 (2000). Yeast Protein Network
  28. 28. Prot P(k) H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001) Topology of the Protein Network
  29. 29. P53 … “ One way to understand the p53 network is to compare it to the Internet. The cell, like the Internet, appears to be a ‘ scale-free network ’.” p53 Network Nature 408 307 (2000)
  30. 30. P53 P(k) p53 Network (mammals)

Hinweis der Redaktion

  • MIGHT GIVE REAL EXAMPLES HERE? FROM WATTS?

×