title: Diffusion on networked systems is a question of time or structure.
abstract: Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalized formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism--network structure, burstiness or fat tails of waiting times--determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal-structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities.
authors.affiliation: ICTEAM and CORE, University of Louvain, 4 Avenue Lemaître, Louvain-la-Neuve B-1348, Belgium.
authors.forename: Jean-Charles
authors.initials: JC
authors.lastname: Delvenne
authors.affiliation: Department of Mathematics and naXys, University of Namur, 8 Rempart de la Vierge, Namur B-5000, Belgium.
authors.forename: Renaud
authors.identifier: 0000000205834595
authors.initials: R
authors.lastname: Lambiotte
authors.affiliation: 1] Department of Mathematics and naXys, University of Namur, 8 Rempart de la Vierge, Namur B-5000, Belgium [2] Department of Public Health Sciences, Karolinska Institutet, 18A Tomtebodavägen, Stockholm S-17177, Sweden.
authors.forename: Luis E C
authors.initials: LE
authors.lastname: Rocha