Distributed Learning Automata-Based Algorithm for Finding K-Clique in Complex Social Networks

Maximal clique finding is a fundamental problem in graph theory and has been broadly investigated. However, maximal clique finding is time-consuming due to its nature and always returns tremendous cliques with large overlap nodes. Hence, a solution uses the relaxed version of the clique called k-clique, which follows up the subset of vertices with size k such that each pair in this subset has an edge. The k-clique problem has several applications in different domains, such as motif detection, finding anomalies in large graphs, and community structure discovery. In this paper, an algorithm based on learning automata is proposed for finding k-clique called (KC-LA) to apply communities in complex social networks. In (KC-LA), a network of learning automata is considering to the underlying networks. Then, select the proper action from a set of allowable actions, the reward and penalty guide KC-LA to detect the k-clique. Also, we applied the k-clique in the concept of finding communities in complex social networks. The KC-LA algorithm is to design some breakthroughs on the real and synthetic graphs in terms of high efficiency and effectiveness.