Biased Random Search in Complex Networks
We study two types of biased random walk on complex networks, which are based on local information. In the first procedure, the transitions towards neighboring nodes with smaller degrees are favored, while in the second another concept based on a two-hop neighborhood is explored. We have verified by numerical simulations that both procedures reduce the mean searching time of the target. We show theoretically that for well connected networks, where nodes have many neighbors, biasing of the random walk based on inverse of nodes' degrees leads to nearly optimal search for undirected and directed networks.