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Semi-Markov random walk on complex networks

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  • Basnarkov, Lasko

Abstract

We present a semi-Markov model of random walk on complex networks in discrete and continuous-time scenario. In the general setting of the semi-Markov chains, the duration of stay at given node – the sojourn time – is random, and the probability to transition to a neighbour depends on the sojourn time. Analytical formulae for the average sojourn time and the node occupation probability of infinite walk are presented for few cases. For the simplest case the theoretical predictions are verified with Monte Carlo simulations. We propose an application of the semi-Markovian random walk for ranking web pages determined by the fraction of time that infinite random surfer spends on a web page – time rank, as an alternative to the existing PageRank that relies on the fraction of visits – visit rank.

Suggested Citation

  • Basnarkov, Lasko, 2026. "Semi-Markov random walk on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015917
    DOI: 10.1016/j.chaos.2025.117578
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    References listed on IDEAS

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    1. Jacques Janssen & Raimondo Manca, 2007. "Semi-markov risk models for finance, insurance and reliability," ULB Institutional Repository 2013/234398, ULB -- Universite Libre de Bruxelles.
    2. Michelitsch, Thomas M. & Polito, Federico & Riascos, Alejandro P., 2021. "On discrete time Prabhakar-generalized fractional Poisson processes and related stochastic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Ryszard Kutner & Jaume Masoliver, 2017. "The continuous time random walk, still trendy: fifty-year history, state of art and outlook," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(3), pages 1-13, March.
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