Enumerating k-Vertex Connected Components in Large Graphs

In social network analysis, structural cohesion (or vertex connectivity) is a fundamental metric in measuring the cohesion of social groups. Given an undirected graph, a k-vertex connected component (k-VCC) is a maximal connected subgraph whose structural cohesion is at least k. A k-VCC has many outstanding structural properties, such as high cohesiveness, high robustness, and subgraph overlapping. In this paper, given a graph G and an integer k, we study the problem of computing all k-VCCs in G. The general idea for this problem is to recursively partition the graph into overlapped subgraphs. We prove the upper bound of the number of partitions, which implies the polynomial running time algorithm for the k-VCC enumeration. However, the basic solution is costly in computing the vertex cut. To improve the algorithmic efficiency, we observe that the key is reducing the number of local connectivity testings. We propose two effective optimization strategies, namely neighbor sweep and group sweep, to significantly reduce the number of local connectivity testings. We conduct extensive performance studies using ten large real datasets to demonstrate the efficiency of our proposed algorithms. The experimental results demonstrate that our approach can achieve a speedup of up to two orders of magnitude compared to the state-of-the-art algorithm.