On the Ability of Graph Coloring Heuristics to Find Substructures in Social Networks

Social network is a graph G = [V,E], in which each vertex from V corresponds to a person and each edge from E describes, that two persons know each other. Social substructure of size m is defined as a clique Km in social network G with m of its vertices. In other words, in a social substructure, everybody knows everybody. In this paper, we study the complementary graph G, in which edges represent persons, who do not know each other. By solving the graph coloring problem with a proper heuristic over this graph, one can find social substructures without any additional information. We define this strategy as the uninformed approach to substructure discovery. Thus, the natural interpretation is assigned to the substructures by user of the method. Our experiments were performed using a well-known tabu search algorithm for the graph coloring problem, called TabuCol [6]. Experimental results are presented on several artificial social networks and one instance of real data.