Optimal local community detection in social networks based on density drop of subgraphs

Abstract

The determination of community structures within social networks is a significant problem in the area of data mining. A proper community is usually defined as a subgraph with a higher internal density and a lower crossing density with others subgraphs. Hierarchical clustering algorithms produce a set of nested clusters, sometimes called dense subgraphs, organized as a hierarchical system and the output is always referred as a dendrogram. However, determining which of clusters in the dendrogram will be selected to form communities in the final output is a difficult problem. Most implementations of data mining algorithms require expert guidance in the implementation of the algorithm in order to establish the appropriate selection of such communities, and ultimately the output may not be optimized as with fixed height tree-cutting algorithms. In this paper, a novel algorithm for community selection is proposed. The intuition of our approach is based on drops of densities between each pair of parent and child nodes on the dendrogram – the higher the drop in density, the higher probability the child should form an independent community. Based on the Max-Flow Min-Cut theorem, we propose a novel algorithm which can output an optimal set of local communities automatically. In addition, a faster algorithm running in linear time is also presented for the case that the dendrogram is a tree. Finally, we validate this approach through a variety of data sets ranging from synthetic graphs to real world benchmark data sets.