COMMUNITY STRUCTURE DISCOVERY IN DIRECTED GRAPHS BY ASYMMETRIC CLUSTERING

A familiar problem with respect to the analysis of network data (in which relations between objects can be described by links between the vertices of a graph) is the discovery of so-called community structures, i.e., the detection of subgraphs of closely connected vertices with comparatively few links joining vertices of different subgraphs. For this task modularity is a popular goodness-of-fit-index. While undirected graphs restrict considerations to basically symmetric relations, more realistic situations can be described by directed graphs. In this paper we consider shortest walk lengths between all pairs of vertices as dissimilarities instead of just using the adjacency information given by the directed edges of the graphs, which enables us to suggest a new approach in which the application of asymmetric clustering is a main step. This enrichment of the underlying adjacency matrix to a walk-length based dissimilarity matrix together with asymmetric hierarchical clustering are the keys of our proposed approach to community structure discovery in directed graphs. We use example graphs from the literature with known modularity values and apply computer-generated directed benchmark graphs for the evaluations. The findings show that our approach compares favourably with results available from the literature.