Efficient structural graph clustering: an index-based approach

Abstract

Graph clustering is a fundamental problem widely applied in many applications. The structural graph clustering ($\mathsf {SCAN}$) method obtains not only clusters but also hubs and outliers. However, the clustering results heavily depend on two parameters, $\epsilon$ and $\mu$, while the optimal parameter setting depends on different graph properties and various user requirements. In addition, all existing $\mathsf {SCAN}$ 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 $\mathsf {SCAN}$. Based on our index, we cluster the graph for any $\epsilon$ and $\mu$ in $O(\sum _{C\in \mathbb {C}}|E_C|)$ time, where $\mathbb {C}$ 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 spent on computing structural clustering depends only on the result size, not on the size of the original graph. Our index’s space complexity is 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 also design an index for I/O efficient query processing. We conduct extensive experiments to evaluate the performance of all our proposed algorithms on 10 real-world networks, with the largest one containing more than 1 billion edges. The experimental results demonstrate that our approaches significantly outperform existing solutions.