Assessing group cohesion in homophily networks

The analysis and exploration of a social network depends on the type of relations at play. Borgatti had proposed a type taxonomy organizing relations in four possible categories. Homophily (similarity) relationships form an important category where relations occur when entities of the network link whenever they exhibit similar behaviors. Examples are networks of co-author, where homophily between two persons follows from co-authorship; or network of actors having played under the supervision of the same movie director, for instance. Homophily is often embodied through a bipartite network where entities of a given type A (authors, movie directors) connect through entities of a different type ℬ (papers, actors). A common strategy is then to project this bipartite graph onto a single-type network with entities of a same type A, possibly weighting edges based on how the type A entities interact with the type ℬ entities underlying the edge. The resulting single-type network can then be studied using standard techniques such as community detection using edge density, or the computation of various centrality indices. This paper revisits this type of approach and introduces a homogeneity measure inspired form past work by Burt. Two entities of type ℬ interact when they both induce a same edge between two entities of type A. The homogeneity of a subgroup thus depends on how intensely and how equally interactions occur between entities of type ℬ giving rise to the subgroup. The measure thus differentiates between subgroups of type A exhibiting similar topologies depending on the interaction patterns of the underlying entities of type ℬ. The method is validated using two widely used datasets. A first example looks at authors of the IEEE InfoVis Conference (InfoVis 2007 Contest). A second example looks at homophily relations between movie actors that have played under the direction of a same director (IMDB).