Listing maximal k-relaxed-vertex connected components from large graphs

Cohesive group extraction is an important task in many applications such as graph visualization, system science, and bioinformatics. The k-vertex-connected component (k-VCC), which is a connected graph that remains connected whenever fewer than k vertices are removed, is a well-studied model for this task. However, the use of k-VCC model may cause resolution issues; thus, we use the k-relaxed-vertex connected component (k-RVCC) model, which effectively eliminates the problem. A k-RVCC is also a connected graph, but to disconnect it, at least n-k vertices must be removed, n is the vertex number of the graph. In this study, we investigate efficient practical algorithms for listing all maximal k-RVCCs from a given graph. Specifically, we first adapted the celebrate Bron-Kerbosch tree-search algorithm from listing cliques to listing k-RVCCs. We then design new branching rules to reduce the number of branches and vertex-cut-based strategies to recursively partition the input graph into smaller independent pieces. Implementation techniques that accelerate the aforementioned algorithms were also investigated. Experiments on various large real networks validated the effectiveness of the proposed algorithms and demonstrated the efficiency of our algorithms in mining cohesive groups.