  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 latent arc strength
stochastic blockmodel for directed interaction networks. We illustrate our
approach studying the interaction between the Kolkata users of the myGamma
mobile network.
