Random walks on stochastic temporal networks

T. Hoffmann, M.A. Porter, R. Lambiotte

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter

Abstract

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.
Original languageEnglish
Title of host publicationUnderstanding Complex Systems
Pages295-313
Number of pages19
DOIs
Publication statusPublished - 1 Jan 2013

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