Biased random walks on complex networks: the role of local navigation rules

TL;DR

This paper analyzes biased random walks on complex networks, deriving exact formulas for stationary probabilities and transit times, and exploring how local navigation rules influence transport efficiency and critical packet generation rates.

Contribution

It provides the first exact analytical expressions for biased random walk metrics on complex networks, enhancing understanding of transport processes and routing protocols.

Findings

Derived exact stationary occupation probabilities

Calculated mean transit times between nodes

Explored the impact of cyclic search on transit times

Abstract

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability, and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper give the basis for theoretical treatment of the transport-related problems on complex networks, including quantitative estimation of the critical value of the packet generation rate.