Clustering and Centrality for Graph VisualizationSergio Camelocamelo@stanford.edu

ProblemOne of the most common techniques for graphvisualization is force-directed drawing. It consistsin associating the graph to a mechanical systemand then finding a low-energy equilibrium stateof it.

In this work we build on top of the d3-force en-gine to emphasize centrality and commu-nity structure of the graph. To do so weconstruct new forces and exploit color, size andcontext.

MotivationCentrality measures reveal the "most important"nodes of a graph (which could refer to the most cen-tral, the most popular, or the most powerful nodes,depending on the definition), while community de-tection attempts to find a "natural partition" of thegraph into different communities

Both properties are very important to understandgraph structure, but they are usually not built intograph visualization engines. Even if they are, theyusually do not interact with the visualization as newforces (i.e. do not interact with position), but onlywith color and size.

Figure 1: Force-directed visualization of Les-Miserables

ClusteringWe detect communities through modularity opti-mization. Communities are color-coded and theycan be exploded with a ctrl-click to reveal innerstructure.

Figure 2: Visualizing Clusters, the exploded community corre-sponds to the enemies of Valjean, the main character

CentralityWe calculate centrality using the page-rank algo-rithm. We also calculate personalized page-rankcentrality, which can be activated by clicking on anynode.

Figure 3: Personalized page-rank for the character Marius, big-ger nodes correspond to characters that are more central to him

InterfaceThe user gets context by hovering over each node to get a description of the character. We include a clusteringforce, which repels nodes from different communities, and a gravity force, that attracts more central nodes tothe center of the graph. The user can set the strength of these forces, and the average edge length.

ConclusionCentrality and community detection improve the un-derstanding of network data, especially if context isprovided (otherwise, it is difficult to explain parti-tions and importance). Results, however, rely a loton using appropriate algorithms. In the case of LesMiserables data, for example, few algorithms gaveas good results as modularity maximization.

Color and node size show an improvement over theraw force-directed graph. It is not clear, however,that forces like gravity and cluster repulsion allowus to identify new information.

Future WorkSome fruitful direction of future research are:• Implementing fast centrality and clusteringalgorithms for big graphs

•Building a fast approximate Verlet integrationengine for graphs on many nodes

•Creating graphs from web data, whileautomatically extracting context information

References[1] B. Baingana, G. Giannakis. Embedding Graphs under Cen-trality Constraints for Network Visualization. arXiv:1401.4408[2] M. Banniester, D. Eppstein, M. Goodrich, L. Trott. Force-Directed Graph Drawing Using Social Gravity and Scaling.arXiv:1209.0748[3] M. Bostock. D3 force-engine. https://github.com/d3/d3-force.[4] M. Bostock. Les-Miserables graph. https://bl.ocks.org/-mbostock/4062045