network visualization: fine-tuning layout techniques for different types of networks

Network visualization: Fine-tuning

layout techniques for different types of

networks

Nees Jan van Eck and Ludo Waltman

Centre for Science and Technology Studies (CWTS), Leiden University

Fifth International Workshop on Social Network Analysis (ARS'15)

Capri, Italy, April 30, 2015

VOSviewer

1

Example

2

Layout problem

• How to position the nodes of a network in a 2D

space in an attractive way?

• What do we mean by ‘attractive’?

– Related nodes are located close to each other

– Groups of related nodes are clustered together

– Sufficient empty space between nodes; no overlapping nodes

– ...

• Attractiveness may depend on:

– Type of visualization (static vs. interactive)

– Type of network (small vs. large; sparse vs. dense)

3

VOS (visualization of similarities)

layout technique

• Quality function to be minimized:

xi: Location of node i in 2D space

aij: Weight of edge between nodes i and j

α and β: Attraction and repulsion parameters (α > β)

• Traditional VOS layout technique is obtained by

setting α = 2 and β = 1

• Technique similar to LinLog (Noack, 2009) is

obtained by setting α = 1 and β = 0

4

ji

β

ji

ji

α

jiijn

βa

αQ xxxxxx

11),,(

1

Co-authorship network

5

α = 2

α = 3

α = 4

α - β = 5 α - β = 4 α - β = 3 α - β = 2 α - β = 1


(attraction = 2, repulsion = 1)

6



7


(attraction = 2, repulsion = -1)

8


(attraction = 2, repulsion = -2)

9

Citation network of journals

10

α = 1

α = 2

α = 3

α - β = 4 α - β = 3 α - β = 2 α - β = 1



11



12



13



14



15

Systematic layout comparison using a

meta criterion

• Meta criterion of Chen and Buja (2009) can be used

to set the attraction and repulsion parameters:

1. For each node, select the k most strongly related nodes

2. For each node, select the k nearest neighbors in the 2D space

3. Calculate the overlap of the two sets of nodes

4. Meta criterion equals the sum of the overlap over all nodes

• We set k = 25

16

Network data

• Bibliometric networks:

– Co-authorship networks

– Citation networks

– Co-citation networks

– Bibliographic coupling networks

– Co-occurrence networks

• Other networks:

– Zachary's karate club

– Les Miserables

– American College football

– Dolphin social network

– US political books

– Power grid

17

Optimal attraction and repulsion

values according to meta criterion

18

Network Attraction Repulsion

Author bib. coup. 1 0

Author cocitation 1 0

Journal citation 1 0

Journal cocitation 1 1 0

Journal cocitation 2 1 0

Term cooccurrence 1 0

Univ. coauthorship 1 0

Publication citation 1 -1

Author coauthorship 1 -3

Network Attraction Repulsion

Football 1 0

Dolphins 1 -1

Les Miserables 1 -1

Political books 1 -1

Power grid 1 -1

Karate club 1 -4

Conclusions

• Attraction = 2 and repulsion = 1 (default values)

usually work reasonably well both for static and for

interactive visualization

• Attraction = 1 and repulsion = 0 (LinLog) often yield

best layout for interactive visualization

• Very sparse networks (e.g., co-authorship) may

benefit from a negative repulsion

• Low repulsion leads to more uniform and less

clustered layouts, which may be attractive for static

visualization

19

Thank you for your attention!

20

References

Chen, L.S., & Buja, A. (2009). Local multidimensional scaling for

nonlinear dimension reduction, graph drawing, and proximity

analysis. Journal of the American Statistical Association, 104(485),

209–219. http://dx.doi.org/10.1198/jasa.2009.0111

Noack, A. (2009). Modularity clustering is force-directed layout. Physical

Review E, 79(2), 026102.

http://dx.doi.org/10.1103/PhysRevE.79.026102

Van Eck, N.J., & Waltman, L. (2010). Software survey: VOSviewer, a

computer program for bibliometric mapping. Scientometrics, 84(2),

523-538. http://dx.doi.org/10.1007/s11192-009-0146-3

Van Eck, N.J., Waltman, L., Dekker, R., & Van den Berg, J. (2010). A

comparison of two techniques for bibliometric mapping:

Multidimensional scaling and VOS. JASIST, 61(12), 2405–2416.

http://dx.doi.org/10.1002/asi.21421

21

http://dx.doi.org/10.1198/jasa.2009.0111

http://dx.doi.org/10.1103/PhysRevE.79.026102

http://dx.doi.org/10.1007/s11192-009-0146-3

http://dx.doi.org/10.1002/asi.21421

Network statistics

22

NetworkNo.

nodes

No.

edgesDensity

Avg.

degree

St. dev.

degreeRadius Diameter

Avg.

path

length

Avg.

clustering

coefficient

Global

clustering

coefficient

Author bib. coup. 174 11739 0.780 134.93 34.38 2 3 1.22 0.89 0.72

Author coauthorship 242 562 0.019 4.64 4.07 6 12 4.87 0.56 0.17

Author cocitation 552 49090 0.323 177.86 86.24 2 3 1.68 0.58 0.27

Journal citation 5000 1155096 0.092 462.04 352.36 2 4 1.94 0.42 0.16

Journal cocitation 1 420 38188 0.434 181.85 73.20 1 2 1.57 0.64 0.31

Journal cocitation 2 232 4112 0.153 35.45 20.41 2 4 1.97 0.49 0.18

Pub. citation 1955 5636 0.003 5.77 6.22 10 18 5.59 0.13 0.05

Term cooccurrence 597 51186 0.288 171.48 92.41 2 2 1.71 0.53 0.22

Univ. coauthorship 500 103870 0.833 415.48 64.83 1 2 1.17 0.88 0.69

Network statistics

23

NetworkNo.

nodes

No.

edgesDensity

Avg.

degree

St. dev.

degreeRadius Diameter

Avg.

path

length

Avg.

clustering

coefficient

Global

clustering

coefficient

Karate club 34 78 0.139 4.59 3.88 3 5 2.41 0.57 0.10

Les Miserables 77 254 0.087 6.60 6.04 3 5 2.64 0.57 0.25

Football 115 613 0.094 10.66 0.89 3 4 2.51 0.40 0.19

Dolphins 62 159 0.084 5.13 2.96 5 8 3.36 0.26 0.13

Political books 105 441 0.081 8.40 5.47 4 7 3.08 0.49 0.15

Power grid 4941 6594 0.001 2.67 1.79 23 46 18.99 0.08 0.04

network visualization: fine-tuning layout techniques for different types of networks

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