Random Walks on Complex Networks

TL;DR

This paper derives an exact formula for mean first passage time in complex networks, introducing a new centrality measure that predicts how quickly nodes can exchange information during random walks.

Contribution

It presents a novel analytical expression for MFPT and introduces the random walk centrality, linking node properties to information spreading speed.

Findings

Analytical expression for MFPT between nodes.

Random walk centrality predicts information flow efficiency.

Numerical simulations confirm theoretical predictions.

Abstract

We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination number and a characteristic relaxation time, and show that it determines essentially the MFPT. The centrality of a node determines the relative speed by which a node can receive and spread information over the network in a random process. Numerical simulations of an ensemble of random walkers moving on paradigmatic network models confirm this analytical prediction.