Overlapping Communities in Co-purchasing and Social Interaction Graphs: A Memetic Approach

Abstract

Simple undirected graphs can be employed to represent numerous complex systems including those arising in social networks, biological networks, communication networks, transportation routes and several others. An important feature of complex networks is the presence of communities, groups of elements densely connected among them but sparsely linked to the rest of the network. In many cases these communities can be overlapping, with nodes participating in more than one community. In this chapter, we present a memetic algorithm for overlapping community detection. Our approach uses the communities of links to depict the overlapping community structure in a simple undirected graph. The approach uses the line of the original graph interest. We perform modularity optimization to discover the communities of the vertices of the line graph to unveil the overlapping community structure of the network. To assess the quality of our method, we present results in synthetically generated benchmark networks and to exemplify the usefulness of our approach we present two case studies. In the first case study we use a network of characters of the novel “A Storm of Swords” book series “A Song of Ice and Fire”, written by George R. R. Martin; and a second one using a co-purchasing network of luxury items from a brand-centric point of view.