The Strength of Arcs and Edges in Interaction Networks: Elements of a Model-Based Approach

When analyzing interaction networks, it is common to interpret the amount of interaction between two nodes as the strength of their relationship. We argue that this interpretation may not be appropriate, since the interaction between a pair of nodes could potentially be explained only by characteristics of the nodes that compose the pair and, however, not by pair-specific features. In interaction networks, where edges or arcs are count-valued, the above scenario corresponds to a model of independence for the expected interaction in the network, and consequently we propose the notions of arc strength, and edge strength to be understood as departures from this model of independence. We discuss how our notion of arc/edge strength can be used as a guidance to study network structure, and in particular we develop a stochastic blockmodel for directed interaction networks where arc strength is taken as a latent variable. We illustrate our approach by studying the interaction between the Kolkata users of the myGamma mobile social network.