Asymptotic analysis of first passage time in complex networks

TL;DR

This paper derives an asymptotic expression for the mean first passage time in complex networks, showing it is inversely proportional to the destination node's degree, with validation on various network types.

Contribution

It provides a novel asymptotic analysis of first passage times in complex networks, linking MFPT to node degree and network relaxation properties.

Findings

MFPT inversely proportional to node degree

Analytical results match numerical simulations

Applicable to real-world networks with short relaxation time

Abstract

The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\tau\ll N$, the computed mean first passage time (MFPT), which is inverse of the decay rate of FPT distribution, is inversely proportional to the degree of the destination. These results are verified numerically for the paradigmatic networks with excellent agreement. We show that the range of validity of the analytical results covers networks that have short relaxation time and high mean degree, which turn out to be valid to many real networks.