Lévy Walk Navigation in Complex Networks: A Distinct Relation between Optimal Transport Exponent and Network Dimension

T. Weng, Michael Small, J. Zhang, P. Hui

    Research output: Contribution to journalArticle

    12 Citations (Scopus)

    Abstract

    © 2015, Nature Publishing Group. All rights reserved. We investigate, for the first time, navigation on networks with a Lévy walk strategy such that the step probability scales as pij∼dij -α, where dij is the Manhattan distance between nodes i and j, and α is the transport exponent. We find that the optimal transport exponent αopt of such a diffusion process is determined by the fractal dimension df of the underlying network. Specially, we theoretically derive the relation αopt=df+2 for synthetic networks and we demonstrate that this holds for a number of real-world networks. Interestingly, the relationship we derive is different from previous results for Kleinberg navigation without or with a cost constraint, where the optimal conditions are α = df and α = df + 1, respectively. Our results uncover another general mechanism for how network dimension can precisely govern the efficient diffusion behavior on diverse networks.
    Original languageEnglish
    Article number17309
    Pages (from-to)1-9
    Number of pages9
    JournalScientific Reports
    Volume5
    DOIs
    Publication statusPublished - 25 Nov 2015

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