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

TL;DR

This paper introduces a model-based approach to measure the strength of arcs and edges in interaction networks, emphasizing deviations from independence models to better understand network structure.

Contribution

It proposes a novel concept of arc and edge strength as departures from independence, and develops a latent arc strength stochastic blockmodel for directed networks.

Findings

Applied to Kolkata mobile network data.

Demonstrated the utility of the model in real-world interaction analysis.

Provided insights into network structure through strength measures.

Abstract

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.