Random Walks on Stochastic Temporal Networks

  • Till Hoffmann
  • Mason A. Porter
  • Renaud Lambiotte
Part of the Understanding Complex Systems book series (UCS)


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.


Static Network Probability Distribution Function Probability Mass Function Temporal Network Dominant Eigenvector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This chapter is based on [20], which contains additional calculations and numerical simulations. RL would like to acknowledge support from FNRS (MIS-2012-F.4527.12) and Belspo (PAI Dysco). MAP acknowledges a research award (#220020177) from the James S. McDonnell Foundation and a grant from the EPSRC (EP/J001759/1). We thank T. Carletti, J.-C. Delvenne, P. J. Mucha, M. Rosvall, and J. Saramäki for fruitful discussions, and we thank P. Holme for helpful comments in his review of this manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Till Hoffmann
    • 1
  • Mason A. Porter
    • 2
  • Renaud Lambiotte
    • 3
  1. 1.Department of PhysicsUniversity of OxfordOxfordUK
  2. 2.Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute and CABDyN Complexity CentreUniversity of OxfordOxfordUK
  3. 3.Department of MathematicsUniversity of NamurNamurBelgium

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