Close or connected? Distance and connectivity effects on transport in networks

TL;DR

This paper presents an analytical framework for understanding how the mean first-passage time in complex networks depends on target connectivity and source-target distance, revealing distinct behaviors for compact and non-compact random walks.

Contribution

It introduces a novel analytical approach that characterizes MFPT dependence on network topology and walk type, highlighting different scaling behaviors.

Findings

Non-compact walks: MFPT scales with inverse target connectivity.

Compact walks: MFPT depends on source-target distance, target connectivity irrelevant for remote targets.

MFPT behavior varies significantly between compact and non-compact exploration modes.

Abstract

We develop an analytical approach which provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type - compact or non compact - of the random walk. In the case of non compact exploration, we show that the MFPT scales linearly with the inverse connectivity of the target, and is largely independent of the starting point. On the contrary, in the compact case the MFPT is controlled by the source-target distance, and we find that unexpectedly the target connectivity becomes irrelevant for remote targets.