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arXiv · 1903.03653

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

Junhao Peng·Elena Agliari
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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.

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Junhao Peng, Elena Agliari. 2019-03-08. Exact results for the first-passage properties in a class of fractal networks. https://doi.org/10.1063/1.5080481

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