On flexible cohesive subgraph mining

When characterizing the cohesion of a subgraph, many cohesive subgraph models impose various constraints on the relationship between the minimum degree of vertices and the number of vertices in the subgraph. However, the constraints imposed by the clique, quasi-clique and k-core models are so rigid that they cannot simultaneously characterize cohesive subgraphs of various scales in a graph. This paper characterizes the flexibility of a cohesive subgraph model by the constraint it imposes on this relationship and proposes f -constraint core (f -CC), a new model that can flexibly characterize cohesive subgraphs of different scales. We formalize the FlexCS problem that finds r representative f -CCs in a graph that are most diversified. This problem is NP-hard and is even NP-hard to be approximated within |V |^1−ϵ for any ϵ > 0. To solve the problem efficiently, a divide-and-conquer algorithm is proposed together with some effective techniques including f -CC generation, sub-problem filtering, early termination, and index-based connected component retrieval. Extensive experiments verify the flexibility of the f -CC model and the effectiveness of the proposed algorithm.