摘要：We investigate, for the first time, navigation on networks with a Lévy walk strategy such that the step probability scales as p ij ~ 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.
