Exact calculations of first-passage quantities on recursive networks

TL;DR

This paper introduces exact methods for calculating first-passage quantities on self-similar recursive networks, revealing how transport properties depend on source-target distance across various complex network classes.

Contribution

It provides a unified framework for exact calculation of first-passage metrics on diverse recursive networks, extending previous results significantly.

Findings

Exact mean first-passage times depend on source-target distance.

Derived splitting probabilities for multiple targets.

Applicable to a wide range of recursive network types.

Abstract

We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter to characterize transport in complex media. We explicitly perform calculations for different classes of recursive networks (finitely ramified fractals, scale-free (trans)fractals, non-fractals, mixtures between fractals and non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our approach unifies and significantly extends the available results in the field.