Estimation of the Average Search Length of Random Walks in Power-Law Networks

Abstract

In this paper we introduce a model to study random walks in power-law networks with one-hop replication. Basically, this model gives a set of expressions that captures how the knowledge about the network evolves as the random walk traverses the network: how many nodes have been known, either because they or their neighbors have been visited by the random walk. With this, we obtain an expression that gives a good estimation of the average number of hops needed to find some random peer from any other random peer. We denote this metric the average search length, and we deem it can be very useful to evaluate random walk based resource location solutions in P2P networks.