Detecting bases of maximal cliques in a graph

Abstract

Maximal Cliques Enumeration (MCE), as a fundamental problem, has been extensively investigated in many fields, such as social networks, and biological science and so forth. However, the existing research works usually ignore the formation principle of maximal cliques which can help us to speed up the detection of maximal cliques in a graph. This paper pioneers a novel problem on detection of bases of maximal cliques in a graph. We propose a formal concept analysis based approach for detecting the bases of maximal cliques and detection theorem. It is believed that our work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.