Finding maximal quasi-cliques containing a target vertex in a graph

Abstract

Many real-world phenomena such as social networks and biological networks can be modeled as graphs. Discovering dense sub-graphs from these graphs may be able to find interesting facts about the phenomena. Quasi-cliques are a type of dense graphs, which is close to the complete graphs. In this paper, we want to find all maximal quasi-cliques containing a target vertex in the graph for some applications. A quasi-clique is defined as a maximal quasi-clique if it is not contained by any other quasi-cliques. We propose an algorithm to solve this problem and use several pruning techniques to improve the performance. Moreover, we propose another algorithm to solve a special case of this problem, i.e. finding the maximal cliques. The experiment results reveal that our method outperforms the previous work both in real and synthetic datasets in most cases.