Intermittent exploration on a scale-free network

TL;DR

This paper investigates an intermittent random walk on scale-free networks, revealing a non-monotonic relationship between exploration time and walk parameters, influenced by network heterogeneity and degree correlations.

Contribution

It introduces a model combining short-range and long-range jumps on scale-free networks, highlighting heterogeneity effects absent in homogeneous networks.

Findings

Edge coverage time shows a non-monotonic dependence on walk duration.

Optimal walk parameters depend on network assortativity.

Degree distribution estimates can be biased by network correlations.

Abstract

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 $t_w$ and random long-range jumps. While the time the walker needs to cover all the nodes increases with $t_w$, the corresponding time for the edges displays a non monotonic behavior with a minimum for some nontrivial value of $t_w$. This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal $t_w$ 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.