Finding maximal k-edge-connected subgraphs from a large graph

In this paper, we study how to find maximal k-edge-connected subgraphs from a large graph. k-edge-connected subgraphs can be used to capture closely related vertices, and finding such vertex clusters is interesting in many applications, e. g., social network analysis, bioinformatics, web link research. Compared with other explicit structures for modeling vertex clusters, such as quasi-clique, k-core, which only set the requirement on vertex degrees, k-edge-connected subgraph further requires high connectivity within a subgraph (a stronger requirement), and hence defines a more closely related vertex cluster. To find maximal k-edge-connected subgraphs from a graph, a basic approach is to repeatedly apply minimum cut algorithm to the connected components of the input graph until all connected components are k-connected. However, the basic approach is very expensive if the input graph is large. To tackle the problem, we propose three major techniques: vertex reduction, edge reduction and cut pruning. These speed-up techniques are applied on top of the basic approach. We conduct extensive experiments and show that the speed-up techniques are very effective.