In the study of dynamical processes on networks, there has been intense focus on network structure-i.e., the arrangement of edges and their associated weights-but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differentialmaster equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.
|titre||Understanding Complex Systems|
|Nombre de pages||19|
|Etat de la publication||Publié - 1 janv. 2013|