Intermittent exploration on a scale-free network

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration tw and random long-range jumps. While the time the walker needs to cover all the nodes increases with tw, the corresponding time for the edges displays a nonmonotonic behaviour with a minimum for some nontrivial value of tw. This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal tw increases with the degree of assortativity in the network. Depending on the nature of degree correlations and the elapsed time the walker finds an over/under-estimate of the degree distribution exponent.