Clustering Social Networks Using Distance-Preserving Subgraphs

Cluster analysis describes the division of a dataset into subsets of related objects, which are usually disjoint. There is considerable variety among the different types of clustering algorithms. Some of these clustering algorithms represent the dataset as a graph, and use graph-based properties to generate the clusters. However, many graph properties have not been explored as the basis for a clustering algorithm. In graph theory, a subgraph of a graph is distance-preserving if the distances (lengths of shortest paths) between every pair of vertices in the subgraph are the same as the corresponding distances in the original graph. In this paper, we consider the question of finding proper distance-preserving subgraphs, and the problem of partitioning a simple graph into an arbitrary number of distance-preserving subgraphs for clustering purposes. We also present a clustering algorithm called DP-Cluster, based on the notion of distance-preserving subgraphs. One area of research that makes considerable use of graph theory is the analysis of social networks. For this reason we evaluate the performance of DP-Cluster on two real-world social network datasets.