A. P. Riascos, José L. Mateos
We introduce a new strategy of navigation in undirected networks, including regular, random and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary probability distribution, the occupation probability, the mean first passage time and the average time to reach a node on the network. We found that the long-range navigation using the L\'evy random walk strategy, in comparison with the normal random walk strategy, is more efficient to reduce the time to cover the network. The dynamical effect of using the L\'evy walk strategy is to transform a large-world network into a small world. Our exact results provide a general framework that connects two important fields: L\'evy navigation strategies and dynamics in complex networks.
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http://arxiv.org/abs/1206.2898
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