Barycentric Graph Clustering

Clustering is an essential aid to human understanding. In its application to graphs, clustering allows a large graph to be partitioned into pieces that can be studied independently or collapsed to give a coarse picture. More importantly, it can be used to identify coherent subgraphs that bear particular attention. As the size of graphs under examination has continued to increase, it has become increasingly important to devise graph algorithms that scale well. This need is felt particularly for graph clustering and for extracting subgraphs of interest, precisely because human comprehension of large graphs is impractical. This paper presents a family of stochastic methods for clustering graphs into coherent subgraphs. These methods scale linearly with the graph size and do not require a priori specification of the number or size of clusters. After a physical motivation, an exposition of the methods is presented, followed by experimental results on some sample graphs.