Long-Range Navigation on Complex Networks using Lévy Random Walks
arXiv:1206.2898 · doi:10.1103/PhysRevE.86.056110
Abstract
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by Lévy 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 Lévy random walk strategy, compared with the normal random walk strategy, is more efficient at reducing the time to cover the network. The dynamical effect of using the Lévy 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: Lévy navigation strategies and dynamics on complex networks.
6 pages, 3 figures
References in corpus (6)
- Understanding individual human mobility patterns
- Synchronization in complex networks
- The scaling laws of human travel
- Navigability of Complex Networks
- Evolution of optimal Lévy-flight strategies in human mental searches
- Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost/benefit model