# Exact results for the first-passage properties in a class of fractal networks

## TL;DR

This paper derives exact first-passage properties for a class of fractal networks, revealing how their structural parameters influence transport efficiency and linking network topology to polymer models.

## Contribution

It provides exact analytical results for first-passage quantities in fractal networks, connecting structural parameters to transport performance and polymer architecture models.

## Key findings

- Transport efficiency improves with increased clustering and modularity.
- As network size is fixed, increasing n or decreasing t enhances transport performance.
- Asymptotic behavior of first-passage quantities depends on network size and diameter.

## Abstract

In this work we consider a class of recursively-grown fractal networks $G_n(t)$, whose topology is controlled by two integer parameters $t$ and $n$. We first analyse the structural properties of $G_n(t)$ (including fractal dimension, modularity and clustering coefficient) and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time and the Kemeny's constant) and we highlight that their asymptotic behavior is controlled by network's size and diameter. Remarkably, if we tune $n$ (or, analogously, $t$) while keeping the network size fixed, as $n$ increases ($t$ decreases) the network gets more and more clustered and modular, while its diameter is reduced, implying, ultimately, a better transport performance. The connection between this class of networks and models for polymer architectures is also discussed.