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Random walks on complex networks.

Jae Dong Noh·Heiko Rieger
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Abstract

We investigate random walks on complex networks and derive an exact expression for the mean first-passage time (MFPT) between two nodes. We introduce for each node the random walk centrality C, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.

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Jae Dong Noh, Heiko Rieger. 2004-03-18. Random walks on complex networks.. https://doi.org/10.1103/physrevlett.92.118701

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