Efficient structural graph clustering

Abstract

Graph clustering is a fundamental problem widely experienced across many industries. The structural graph clustering (SCAN) method obtains not only clusters but also hubs and outliers. However, the clustering results closely depend on two sensitive parameters, ϵ and μ, while the optimal parameter setting depends on different graph properties and various user requirements. Moreover, all existing SCAN solutions need to scan at least the whole graph, even if only a small number of vertices belong to clusters. In this paper we propose an index-based method for SCAN. Based on our index, we cluster the graph for any ϵ and μ in O (Σ c ϵℂ | E C |) time, where ℂ is the result set of all clusters and | E C | is the number of edges in a specific cluster C. In other words, the time expended to compute structural clustering depends only on the result size, not on the size of the original graph. Our index's space complexity is bounded by O ( m ), where m is the number of edges in the graph. To handle dynamic graph updates, we propose algorithms and several optimization techniques for maintaining our index. We conduct extensive experiments to practically evaluate the performance of all our proposed algorithms on 10 real-world networks, one of which contains more than 1 billion edges. The experimental results demonstrate that our approaches significantly outperform existing solutions.