Journal
EUROPEAN PHYSICAL JOURNAL B
Volume 84, Issue 4, Pages 691-697Publisher
SPRINGER
DOI: 10.1140/epjb/e2011-20834-1
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Funding
- National Natural Science Foundation of China [61074119]
- Hong Kong Research Grants Council under the GRF [CityU 1114/11E]
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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) similar to d (-gamma) , the scaling of the lower bound is N (1-1/gamma) . 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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