Detecting Community Structures in Social Networks by Graph Sparsification

Community structures are inherent in social networks and finding them is an interesting and well-studied problem. Finding community structures in social networks is similar to locating densely connected clusters of nodes in a graph. One of the popular methods for finding communities is to first find the inter-community edges and then removing them to reveal the communities. It is well-known that a network centrality measure named edge betweenness can be used to detect the inter-community edges. The edges with high edge betweenness are those that fall in a large number of shortest paths out of all possible pairs of shortest paths. Finding all-pair shortest paths is a computationally expensive task, especially for large-sized graphs. So we construct a t-spanner, a known graph sparsification technique, for finding edges with high betweenness and eventually find communities by removing such edges. Using the t-spanner, we then detect the inter-community edges in O(km) running time by building a distance oracle of size O(kn1+1/k), where t = 2k-1. Compared to the traditional community detection methods dependent on calculation of betweenness values, our algorithm runs much faster. Experiments show that our algorithm finds communities of quality comparable to the other state-of-the-art community detection algorithms.