complementarity of Persons sharing properties in social networks

Our previous work focused on the unified community detection in networks of people: social networks, communities of actors, etc. shown as generally bipartite graph. In this article. We define therefore the notion of complementarity between the vertices of a bipartite graph. We use for it the concepts of entropy and mutual information. We show the usefulness of such an approach and the value of the approach by an experiment on a well known example.

Complementarity in social networks is an interesting approach to identify cohesion in groups of persons. Our previous works studied a first approach of complementarity in networks represented as bipartite graphs: social networks, communities of actors, etc. In this paper we try to respond to semantic complementarity problems that arise as soon as one wishes to associate people in order to best fulfil a goal. We compare several approaches of complementarity to find the most appropriate technique. In some definitions of complementarity, the problem is viewed as close to a classical research: find transversals in hypergraphs, with however differences in final goals. To validate our approach, we apply and compare our methods on well known graphs and real data whose sizes are very different: from small graphs to very large graphs.