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

Abstract:

: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 α(opt) of such a diffusion process is determined by the fractal dimension df of the underlying network. Specially, we theoretically derive the relation α(opt) = 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.

journal_name

Sci Rep

journal_title

Scientific reports

authors

Weng T,Small M,Zhang J,Hui P

doi

10.1038/srep17309

subject

Has Abstract

pub_date

2015-11-25 00:00:00

pages

17309

issn

2045-2322

pii

srep17309

journal_volume

5

pub_type

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