Mining Maximal Clique Summary with Effective Sampling

Abstract

Maximal clique enumeration (MCE) is a fundamental problem in graph theory and is used in many applications, such as social network analysis, bioinformatics, intelligent agent systems, cyber security. Most existing MCE algorithms focus on improving the efficiency rather than reducing the size of the output, which could consist of a large number of maximal cliques. In this paper, we study how to report a summary of less overlapping maximal cliques. The problem was studied before, however, after examining the pioneer approach, we consider it still not satisfactory. To advance the research along this line, this paper attempts to make two contributions: (a) We propose a more effective sampling strategy, which produces a much smaller summary but still ensures that the summary can somehow witness all the maximal cliques and the expectation of each maximal clique witnessed by the summary is above a predefined threshold. (b) To verify experimentally, we tested ten real benchmark datasets that have a variety of graph characteristics. The results show that our new sampling strategy consistently outperforms the state-of-the-art method by producing smaller summaries and running faster on all the datasets.