Lévy walk navigation in complex networks: a distinct relation between optimal transport exponent and network dimension

摘要

We investigate, for the first time, navigation on networks with a Lévy walk strategy such that the step probability scales as pij; ~ d;ij;–α;, where d;ij; 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 d;f; of the underlying network. Specially, we theoretically derive the relation α;opt; = d;f; + 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 = d;f; and α = d;f + 1;, respectively. Our results uncover another general mechanism for how network dimension can precisely govern the efficient diffusion behavior on diverse networks.;