Order of events taking place in complex networks may dramatically alter the way diffusion occurs

In a paper about to be published in European Physical Journal B, Renaud Lambiotte and Lionel Tabourier from the University of Namur, Belgium, together with Jean-Charles Delvenne from the Catholic University of Louvain, Belgium, show that one key factor that can dramatically change a diffusion process is the order in which events take place in complex networks.

Since it is now possible to gather data on the timings at which edges of a complex network are activated or not, network dynamics can now be studied more precisely. Empirical evidence in a variety of social and biological systems has shown that the time intervals between the activation of edges are such that it occurs in bursts. As a result, there are broad distributions for the times between these activation events.

So far, a majority of works have relied on computer simulations. However, a purely computational approach is unable to provide a general picture of the problem and to identify important structural and temporal properties. Instead, the authors developed an analytical model to better understand the properties of time-dependent networks that either accelerate or slow down diffusion.

Their analytical study focused on different classes of popular models for diffusion, namely random walks -- which is a mathematical description of a path that consists of a succession of random steps -- and epidemic spread models, and found the way in which the temporal ordering of events matters. They expect these results to help in building more appropriate metrics to understand real-world complex network data.