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Effect of memory on the dynamics of random walks on networks
Umeå University, Faculty of Science and Technology, Department of Physics.ORCID iD: 0000-0002-7181-9940
2015 (English)In: Journal of Complex Networks, ISSN 2051-1310, Vol. 3, no 2, p. 177-188Article in journal (Refereed) Published
Abstract [en]

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an analytical expression for the effect of memory on the spectral gap and thus, equivalently, on the characteristic time needed for the stochastic process to asymptotically reach equilibrium. Perturbation analysis shows that standard first-order Markov models can either overestimate or underestimate the diffusion rate of flows across the modular structure of a system captured by a second-order Markov network. We test the theoretical predictions on a toy example and on numerical data, and discuss their implications for network theory, in particular in the case of temporal or multiplex networks.

Place, publisher, year, edition, pages
Oxford University Press, 2015. Vol. 3, no 2, p. 177-188
Keywords [en]
random walks, spectral gap, non-Markovian process, temporal networks
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Other Physics Topics
Identifiers
URN: urn:nbn:se:umu:diva-151314DOI: 10.1093/comnet/cnu017ISI: 000434604700002OAI: oai:DiVA.org:umu-151314DiVA, id: diva2:1244229
Available from: 2018-08-31 Created: 2018-08-31 Last updated: 2018-08-31Bibliographically approved

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Rosvall, Martin

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