Linear-time enumeration of maximal K-edge-connected subgraphs in large networks by random contraction

Capturing sets of closely related vertices from large networks is an essential task in many applications such as social network analysis, bioinformatics, and web link research. Decomposing a graph into k-core components is a standard and efficient method for this task, but obtained clusters might not be well-connected. The idea of using maximal k-edge-connected subgraphs was recently proposed to address this issue. Although we can obtain better clusters with this idea, the state-of-the-art method is not efficient enough to process large networks with millions of vertices. In this paper, we propose a new method to decompose a graph into maximal k-edge-connected components, based on random contraction of edges. Our method is simple to implement but improves performance drastically. We experimentally show that our method can successfully decompose large networks and it is thousands times faster than the previous method. Also, we theoretically explain why our method is efficient in practice. To see the importance of maximal k-edge-connected subgraphs, we also conduct experiments using real-world networks to show that many k-core components have small edge-connectivity and they can be decomposed into a lot of maximal k-edge-connected subgraphs.