arXiv 1306.07152013-06-04physics.soc-phcs.SI

Random Walks on Stochastic Temporal Networks

Till Hoffmann, Mason A. Porter, Renaud Lambiotte

备注：: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulations
DOI：: 10.1007/978-3-642-36461-7_15

英文摘要：

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-differential master 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.

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