This document summarizes a presentation about bibliometric network analysis tools and techniques. It discusses two software tools, VOSviewer and CitNetExplorer, that are used to construct and visualize bibliometric networks. It also outlines various network analysis techniques, including layout algorithms, community detection methods, and a unified approach to mapping and clustering networks. Finally, it provides an analysis of the structure and evolution of the field of network science based on a large bibliometric dataset.

1. Bibliometric network analysis:
Software tools, techniques, and an
analysis of network science at Leiden
University
Ludo Waltman and Nees Jan van Eck
Centre for Science and Technology Studies (CWTS), Leiden University
LCN2 Seminar
Leiden, November 27, 2015

2. Centre for Science and Technology
Studies (CWTS)
• Research center at Leiden University
focusing on science and technology
studies
• About 30 staff members
• History of more than 25 years in
bibliometric and scientometric
research
• Contract research
• Full access to large bibliographic
database (Web of Science and
Scopus)
1

3. Bibliographic databases: ‘Big data’
2
Web of Science Scopus
Journals 12,000 20,000
Publications 45 million 35 million
Citations 1 billion 0.9 billion

4. Bibliometric networks
3
Web of
Science
Scopus
Citation network
of publications
Co-authorship network
of authors / organizations
Co-citation network
of pubs / authors / journals
Co-occurrence network
of terms
Bibliographic coupling network
of pubs / authors / journals
Bibliographic
database

5. Outline
• Software tools
• Network analysis techniques
• Analysis of network science
4

6. Software tools
5

7. Software tools
• VOSviewer (www.vosviewer.com)
– Tool for constructing and visualizing bibliometric networks
• CitNetExplorer (www.citnetexplorer.nl)
– Tool for visualizing and analyzing citation networks of
publications
6

8. VOSviewer
7

9. Map of university co-authorship
network
8

10. Map of journal citation network
9

11. CitNetExplorer
10

12. • Any type of bibliometric
network
• Co-authorship, co-citation, and
bibliographic coupling
• Time dimension is ignored
• Networks of at most ~10,000
nodes are supported
• Only citation networks of
publications
• Direct citation relations
• Time dimension is explicitly
considered
• Millions of publications are
supported
11
VOSviewer CitNetExplorer

13. Network
analysis
techniques
12

14. Network analysis techniques
13
Layout:
• Visualization of similarities
(VOS)
Community detection:
• Weighted modularity
• Smart local moving algorithm

15. 1414
Clustering can be seen as mapping
in a restricted space

16. 1515
Clustering can be seen as mapping
in a restricted space

17. Unified approach to mapping and
clustering
Minimize
where
n: number of nodes in the network
m: total weight of all edges in the network
Aij: weight of edge between nodes i and j
ki: total weight of all edges of node i
16
 

ji
ij
ji
ijij
ji
n ddA
kk
m
xxQ 2
1
2
),,( 
Mapping
xi: vector denoting the location
of node i in a p-dimensional
space


p
k
jkikjiij xxxxd
1
2
)(
Clustering
xi: integer denoting the
community to which node i
belongs
: resolution parameter






ji
ji
ij
xx
xx
d
if1
if0


18. Unified approach: Clustering
Equivalent to a weighted variant of modularity-based
community detection (Waltman et al., 2010)
Maximize
where
(xi, xj) equals 1 if xi = xj and 0 otherwise
17








ji
ji
ijijjin
m
kk
Awxx
m
xxQ
2
),(
2
1
),,(ˆ 1 
ji
ij
kk
m
w
2


19. Unified approach: Mapping
• Equivalent to the VOS (visualization of similarities)
technique (Van Eck & Waltman, 2007)
• Limit case of multidimensional scaling (Van Eck et
al., 2010)
18
 

ji
ji
ji
jiij
ji
xxxxA
kk
m
Q
22
 

ji
jiijij xxDW
2

1
2

 ij
ji
ij A
m
kk
D ij
ji
ij A
kk
m
W
2

VOS
MDS

20. Unified approach
Commonly used clustering technique (modularity)
and commonly used mapping technique (MDS) can be
brought together in a unified framework
19
Unified
approach
Modularity
(weighted)
VOS
MDS
(limit case)

21. Louvain algorithm
• ‘Louvain algorithm’ (Blondel et al., 2008) is the
most popular heuristic algorithm for large-scale
modularity optimization
20

22. Louvain algorithm
21
Q = 0.3791
Q = 0.4151
Local
moving
heuristic
Local moving heuristic
Reduced
network
Original
network

23. Smart local moving algorithm
• Smart local moving algorithm extends the Louvain
algorithm in two ways:
1. Multiple algorithm iterations, with output of one iteration
serving as input for the next iteration
2. Recursive application of the local moving heuristic
22

24. Smart local moving algorithm
23
Q = 0.4198
Q = 0.3791
Reduced
network
Local moving
heuristic in
subnetworks
Local moving heuristic
Original
network

25. Empirical comparison (large networks)
• 6 networks
• Algorithms:
– Louvain (1 iteration)
– Louvain (10 iterations)
– Smart local moving (10 iterations)
• 10 algorithm runs using different random numbers
24

26. Empirical comparison (large networks)
25
Network Louvain Louvain (iterative) Smart local moving
Amazon
(0.5M / 0.9M)
Qmin 0.9257 0.9293 0.9335
Qmax 0.9264 0.9299 0.9338
t 6 9 28
DBLP
(0.4M / 1.0M)
Qmin 0.8203 0.8243 0.8357
Qmax 0.8227 0.8271 0.8367
t 7 9 26
IMDb
(0.4M / 15.0M)
Qmin 0.6976 0.6994 0.7050
Qmax 0.7041 0.7052 0.7077
t 18 26 100
LiveJournal
(4.0M / 34.7M)
Qmin 0.7441 0.7578 0.7676
Qmax 0.7557 0.7658 0.7720
t 350 566 1 549
WoS
(10.6M / 104.5M)
Qmin 0.7714 0.7851 0.7918
Qmax 0.7786 0.7902 0.7957
t 6 800 8 398 19 994
Web uk-2005
(39.5M / 783.0M)
Qmin 0.9793 0.9796 0.9801
Qmax 0.9795 0.9797 0.9801
t 11 006 11 736 17 074

27. Large-scale
analysis of the
structure of
science
26

28. Algorithmic classification systems of
science
• Publications (not journals) are clustered into
research areas based on citation relations
• Research areas are defined at different levels of
granularity and are organized hierarchically
• Clustering is performed using the smart local
moving algorithm (improved Louvain algorithm;
Waltman & Van Eck, 2013)
27

29. Algorithmically constructed
classification system of science
• 16.2 million publications from the period 2000–
2014 indexed in Web of Science
• 241.7 million citation relations
• Classification system of 3 hierarchical levels:
– 28 broad disciplines
– 813 fields
– 3,822 subfields
28

30. Breakdown of scientific literature into
3822 subfields
30
Social sciences
and humanities
Biomedical and
health sciences
Life and earth
sciences
Physical
sciences and
engineering
Mathematics and
computer science

31. Publications in scientometrics
subfield
31

32. Time-line map of highly cited
scientometrics publications
32

33. Application: Exploring the interface
between physical and medical sciences
33

34. Application: Emerging research areas
in physics
35
Particle physics
Astronomy and
astrophysics
Optics
Applied physics
Atomic, molecular,
and chemical
physics
Condensed matter
physics

35. CWTS Leiden Ranking
36

36. Analyzing the
structure and
evolution of
network
science
37

37. Network science according to
Wikipedia
Network science is an interdisciplinary academic field
which studies complex networks such as
telecommunication networks, computer networks,
biological networks, cognitive and semantic networks,
and social networks. The field draws on theories and
methods including graph theory from mathematics,
statistical mechanics from physics, data mining and
information visualization from computer science,
inferential modeling from statistics, and social
structure from sociology.
38

38. Networks text book by Mark Newman
The scientific study of networks, including computer
networks, social networks, and biological networks,
has received an enormous amount of interest in the
last few years. (...) The study of networks is broadly
interdisciplinary and important developments have
occurred in many fields, including mathematics,
physics, computer and information
sciences, biology, and the social sciences.
39

39. Journal of Complex Networks
The journal covers everything from the basic
mathematical, physical and computational principles
needed for studying complex networks to their
applications leading to predictive models in
molecular, biological, ecological, informational,
engineering, social, technological and other systems.
40

40. Network Science journal
Network Science is a new journal for a new discipline -
one using the network paradigm, focusing on actors
and relational linkages, to inform research,
methodology, and applications from many fields
across the natural, social, engineering and
informational sciences.
41

41. Popular network terms
42
neural network
social network
wireless sensor
network
complex network
wireless network
regulatory
network

42. Network publications
• Web of Science database
• Time period 1992–2014
• Research articles and review articles
• ‘network’ or ‘graph’ in title or abstract
• 0.7 million publications
43

43. Number of network publications per
year
44

44. Co-occurrence relations between terms
in network publications
45
Biology
Neuroscience
Social science
Chemistry
Mathematics
Computer science

45. Co-occurrence relations between terms
in network publications
46
Biology
Neuroscience
Social science
Chemistry
Mathematics
Computer science

46. Network fields
• Network publications are clustered into fields
• Based on 3.1 million citation relations between
network publications
• Clustering methodology of Waltman and Van Eck
(2012, 2013)
• Publications in the same journal are assigned to the
same cluster, except for multidisciplinary journals
• 13 main clusters, covering 97% of all 0.7 million
network publications
47

47. Number of network publications per
field
48

48. Citation relations between journals
with ≥ 100 network publications
49
Computer science
Mathematics
Physics
Neuroscience
Biology
Chemistry

49. Convergence toward an integrated
network science field?
Number of citations between network fields
(x 100; 5-year citation window)
50
2004
Physics
Math
CS
Biology SSNeuro
3 2
2 7 4 2 1 2
Physics
Math
CS
Biology SSNeuro
10 5
10 13 9 9 8 5
2014
2
5 27
6 39 1

50. Convergence toward an integrated
network science field?
% of publications in each of two fields citing at least one
publication in the other field (5-year citation window)
51
2004
Physics
Math
CS
Biology SSNeuro
3 4
2 6 5 3 2 2
Physics
Math
CS
Biology SSNeuro
5 5
3 6 3 5 4 5
2014
6 10
7 12

51. Convergence of social science and
physics
52

52. Citation relations between journals at
the SS-physics interface (2005–2014)
53
Scientometrics
Economics
Sociology and SNA
Physica A
PRE PRL
PLOS ONE
PNAS
Nature
Science
Sci. Rep.
JSTAT
EPL
EPJ B

53. Leiden University’s institutes with most
publications on network science
• LUMC
• Leiden Institute of Advanced Computer Science (Science)
• Leiden Institute of Chemistry (Science)
• Leiden Institute of Physics (Science)
• Institute of Psychology (FSW)
• Mathematical Institute (Science)
• Leiden Observatory (Science)
• Institute of Biology Leiden (Science)
• Centre for Science and Technology Studies (FSW)
54

54. Citation relations between journals
with ≥ 100 network publications
55
Computer science
Mathematics
Physics
Neuroscience
Biology
Chemistry

55. Leiden University’s publication output
in network science journals
56

56. Leiden University’s publication output
in network science journals
57
CWTS
Leiden Institute
of Chemistry
LIACS
Leiden Institute
of Physics
Leiden Institute
of Physics
Institute of
Psychology
LUMC
Institute of
Biology Leiden
Mathematical
Institute

57. Conclusions
• Network research has increased tremendously
during the past 10–15 years
• Network research covers many fields of science,
but there is only limited evidence of increasing
integration
• Network research in social science and physics is
becoming more connected
• Leiden University contributes to all major areas of
network research, although the contribution to in
the area of computer science is somewhat modest
58

58. Do it yourself!
59
www.vosviewer.com www.citnetexplorer.nl

59. Thank you for your attention!
60