Mean first-passage time for maximal-entropy random walks in complex networks

TL;DR

This paper analyzes the mean first-passage time (MFPT) for maximal-entropy random walks in complex networks, deriving explicit formulas and comparing their efficiency to traditional random walks, revealing conditions where each is more effective.

Contribution

It provides a new explicit expression for MFPT in MERW based on eigenvalues and eigenvectors, and evaluates its scaling behavior in uncorrelated scale-free networks.

Findings

MFPT to a hub node is lower for MERW than TURW

MFPT to low-degree or random nodes is higher for MERW

MFPT insights inform search efficiency in complex networks

Abstract

We perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we derive an explicit expression of MFPT in terms of the eigenvalues and eigenvectors of the adjacency matrix associated with the network. For MERW in uncorrelated networks, we also provide a theoretical formula of MFPT at the mean-field level, based on which we further evaluate the dominant scalings of MFPT to different targets for MERW in uncorrelated scale-free networks, and compare the results with those corresponding to traditional unbiased random walks (TURW). We show that the MFPT to a hub node is much lower for MERW than for TURW. However, when the destination is a node with the least degree or a uniformly chosen node, the MFPT is higher for MERW than for TURW. Since MFPT to a uniformly chosen node measures real efficiency of search in networks, our work provides insight into general searching process in complex networks.