This paper presents a method for identifying a set of dense subgraphs of a given sparse graph. Within the main applications of this dense subgraph problem, the dense subgraphs are interpreted as communities, as in, e.g., social networks. The problem of identifying dense subgraphs helps analyze graph structures and complex networks and it is known to be challenging. It bears some similarities with the problem of reordering/blocking matrices in sparse matrix techniques. We exploit this link and adapt the idea of recognizing matrix column similarities, in order to compute a partial clustering of the vertices in a graph, where each cluster represents a dense subgraph. In contrast to existing subgraph extraction techniques which are based on a complete clustering of the graph nodes, the proposed algorithm takes into account the fact that not every participating node in the network needs to belong to a community. Another advantage is that the method does not require to specify the number of clusters; this number is usually not known in advance and is difficult to estimate. The computational process is very efficient, and the effectiveness of the proposed method is demonstrated in a few real-life examples.
|Number of pages
|IEEE Transactions on Knowledge and Data Engineering
|Published - 2012
Bibliographical noteFunding Information:
This research was supported by US National Science Foundation (NSF) grant DMS-0810938 and by the Minnesota Supercomputer Institute. The first author was supported in part by a University of Minnesota Doctoral Dissertation Fellowship. The authors would like to thank Arindam Banerjee for introducing them to the dense subgraph problem and in particular for bringing to their attention the importance of finding a partial clustering of the graph vertices.
- Dense subgraph
- hierarchical clustering
- matrix reordering
- partial clustering
- social network