Walks on Apollonian networks

Abstract

We carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square displacement, and the network coverage for unrestricted random walk. The diffusions both on DANs and RANs are proved to be sublinear. The search efficiency for walks with various strategies and the influence of the topology of underlying networks on the dynamics of walks are discussed. Contrary to one's intuition, it is shown that the self-avoiding random walk, which has been verified as an optimal strategy for searching on scale-free and small-world networks, is not the best strategy for the DAN in the thermodynamic limit.

arXiv comment5 pages, 4 figures

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Cited by in corpus (12)

• Global mean first-passage times of random walks on complex networks
• Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect
• Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices
• Explicit determination of mean first-passage time for random walks on deterministic uniform recursive trees
• Random walks on the Apollonian network with a single trap
• Close or connected? Distance and connectivity effects on transport in networks
• Correlations in random Apollonian network
• Generalized open quantum walks on Apollonian networks
• Vertex labeling and routing in expanded Apollonian networks
• Efficient network exploration by means of resetting self-avoiding random walkers
• Displacement of transport processes on networked topologies
• Markov chain approach to anomalous diffusion on Newman-Watts networks