Towards k-vertex connected component discovery from large networks

In many real life network-based applications such as social relation analysis, Web analysis, collaborative network, road network and bioinformatics, the discovery of components with high connectivity is an important problem. In particular, k-edge connected component (k-ECC) has recently been extensively studied to discover disjoint components. Yet many real scenarios present more needs and challenges for overlapping components. In this paper, we propose a k-vertex connected component (k-VCC) model, which is much more cohesive, and thus supports overlapping between components very well. To discover k-VCCs, we propose three frameworks including top-down, bottom-up and hybrid frameworks. The top-down framework is first developed to find the exact k-VCCs by dividing the whole network. To further reduce the high computational cost for input networks of large sizes, a bottom-up framework is then proposed to locally identify the seed subgraphs, and obtain the heuristic k-VCCs by expanding and merging these seed subgraphs. Finally, the hybrid framework takes advantages of the above two frameworks. It exploits the results of bottom-up framework to construct the well-designed mixed graph and then discover the exact k-VCCs by contracting the mixed graph in a top-down way. Because the size of mixed graph is smaller than the original network, the hybrid framework runs much faster than the top-down framework. Comprehensive experimental are conducted on large real and synthetic networks and demonstrate the efficiency and effectiveness of the proposed exact and heuristic approaches.