Close or connected? Distance and connectivity effects on transport in networks

Abstract

We develop an analytical approach which provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type - compact or non compact - of the random walk. In the case of non compact exploration, we show that the MFPT scales linearly with the inverse connectivity of the target, and is largely independent of the starting point. On the contrary, in the compact case the MFPT is controlled by the source-target distance, and we find that unexpectedly the target connectivity becomes irrelevant for remote targets.

7 pages, 7 figures

References in corpus (16)

• Critical phenomena in complex networks
• First-passage times in complex scale-invariant media
• How to calculate the fractal dimension of a complex network: the box covering algorithm
• Scaling theory of transport in complex networks
• Fractal and Transfractal Recursive Scale-Free Nets
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Exact mean first-passage time on the T-graph
• Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Random walks on complex trees
• Trapping in complex networks
• Diffusion Processes on Power-Law Small-World Networks
• Scaling of disordered recursive networks
• Random Walks on Complex Networks

Cited by in corpus (14)

• First passage time for random walks in heterogeneous networks
• Mean first-passage time for random walks on undirected networks
• Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks
• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Random walks in modular scale-free networks with multiple traps
• Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks
• Role of fractal dimension in random walks on scale-free networks
• Origin of the hub spectral dimension in scale-free networks
• Effects of reciprocity on random walks in weighted networks
• Trapping in and escape from branched structures of neuronal dendrites
• Exact eigenvalue spectrum of a class of fractal scale-free networks
• Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap
• Discrete-time model for a substance motion in a channel of a network. Application to a human migration channel
• Heterogeneous Mean First-Passage Time Scaling in Fractal Media