Finding and Visualizing Graph Clusters Using PageRank Optimization

We give algorithms for finding graph clusters and drawing graphs, highlighting local community structure within the context of a larger network. For a given graph G, we use the personalized Page Rank vectors to determine a set of clusters, by optimizing the jumping parameter alpha subject to several cluster variance measures in order to capture the graph structure according to Page Rank. We then give a graph visualization algorithm for the clusters using Page Rank-based coordinates. Several drawings of real-world data are given, illustrating the partition and local community structure.