Fundamental Structures in Dynamic Communication Networks

In this paper I introduce a framework for modeling temporal communication networks and dynamical processes unfolding on such networks. The framework originates from the realization that there is a meaningful division of temporal communication networks into six dynamic classes, where the class of a network is determined by its generating process. In particular, each class is characterized by a fundamental structure: a temporal-topological network motif, which corresponds to the network representation of communication events in that class of network. These fundamental structures constrain network configurations: only certain configurations are possible within a dynamic class. In this way the framework presented here highlights strong constraints on network structures, which simplify analyses and shape network flows. Therefore the fundamental structures hold the potential to impact how we model temporal networks overall. I argue below that networks within the same class can be meaningfully compared, and modeled using similar techniques, but that integrating statistics across networks belonging to separate classes is not meaningful in general. This paper presents a framework for how to analyze networks in general, rather than a particular result of analyzing a particular dataset. I hope, however, that readers interested in modeling temporal networks will find the ideas and discussion useful in spite of the paper's more conceptual nature.