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arXiv · 1111.1500

Mean first-passage time for random walks on undirected networks

Zhongzhi Zhang·Alafate Julaiti·Baoyu Hou·Hongjuan Zhang·Guanrong Chen
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Abstract

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-γ}$, the scaling of the lower bound is $N^{1-1/γ}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.

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BibTeXRIS

Zhongzhi Zhang, Alafate Julaiti, Baoyu Hou, Hongjuan Zhang, Guanrong Chen. 2011-11-07. Mean first-passage time for random walks on undirected networks. https://doi.org/10.1140/epjb%2Fe2011-20834-1

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