Global Similarity in Social Networks with Typed Edges

Most real-world social network analysis treats edges (relationships) as having different intensities (weights), but the same qualitative properties. We address the problem of modelling edges of qualitatively different types that nevertheless interact with one another. For example, influence flows along friend and colleagues edges differently, but treating the two sets of different kinds of edges as independent graphs surely misses interesting and useful structure. We model the sub graph corresponding to each edge type as a layer, and show how to weight the edges connecting the layers to produce a consistent spectral embedding, including for directed graphs. This embedding can be used to compute social network properties of the combined graph, to predict edges, and to predict edge types. We illustrate with Padgett´s dataset of Florentine families in the 15th Century.