Entanglement in Multiplex Networks: Understanding Group Cohesion in Homophily Networks

Abstract

The analysis and exploration of a social network depends on the type of relations at play. Homophily (similarity) relationships form an important category of relations linking entities whenever they exhibit similar behaviors. Examples of homophily networks examined in this paper are: co-authorship, where homophily between two persons follows from having co-published a paper on a given topic; movie actors having played under the supervision of the same movie director; members of a entrepreneur network having exchanged ideas through discussion threads. Homophily is often embodied through a bipartite network where entities (authors, movie directors, members) connect through attributes (papers, actors, discussion threads). A common strategy is then to project this bipartite graph onto a single-type network. The resulting single-type network can then be studied using standard techniques such as community detection or by computing various centrality indices. We revisit this type of approach and introduce a homogeneity measure inspired from past work by Burt and Schøtt. Instead of considering a projection in a bipartite network, we consider a multiplex network which preserves both entities and attributes as our core object of study. The homogeneity of a subgroup depends on how intensely and how equally interactions occur between layers of edges giving rise to the subgroup. The measure thus differentiates between subgroups of entities exhibiting similar topologies depending on the interaction patterns of the underlying layers. The method is first 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). A third example shows the capability of the methodology to deal with weighted homophily networks, pointing at subtleties revealed from the analysis of weights associated with interactions between attributes.