Covering K-Cliques in Billion-Scale Graphs

The k-clique structure in graphs has been investigated in various real-world applications, such as community detection in complex networks, functional module discovery in biological networks, and link spam detection in web graphs. Despite extensive research on k-clique enumeration, the large number of k-cliques in many graphs poses a challenge for practical application and computation. To address this, we explore the k-clique τ-cover problem, a generalization of the vertex cover problem. The problem aims to find a small set of vertices that can effectively represent all k-cliques in the graph. We prove the NP-hardness of finding the minimum k-clique cover. We propose a hierarchical solution that computes a small cover without enumerating k-cliques. Extensive experiments on real-world graphs verify the efficiency and effectiveness of our solution.