Bruno Ribeiro, Nicola Perra, Andrea Baronchelli
Time-varying networks describe a wide array of systems whose constituents and interactions evolve in time. These networks are defined by an ordered stream of interactions between nodes. However, they are often represented as a sequence of static networks, resulting from aggregating all edges and nodes appearing at time intervals of size \Delta t. In this work we investigate the consequences of this procedure. In particular, we address the impact of an arbitrary \Delta t on the description of a dynamical process taking place upon a time-varying network. We focus on the elementary random walk, and put forth a mathematical framework that provides exact results in the context of synthetic activity driven networks. Remarkably, the equations turn out to also describe accurately the behavior observed on real datasets. Our results provide the first analytical description of the bias introduced by time integrating techniques, and represent a step forward in the correct characterization of dynamical processes on time-varying graphs.
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http://arxiv.org/abs/1211.7052
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