Mesoscopics and fluctuations in networks

TL;DR

This paper investigates mesoscopic fluctuations in finite-size networks with complex degree distributions, revealing Poissonian fluctuation spectra and emphasizing their significance in networks with fat-tailed degree distributions.

Contribution

It introduces an analysis of mesoscopic fluctuations in networks, highlighting their Poissonian nature and importance in large-degree and fat-tailed degree distribution networks.

Findings

Fluctuations in the number of vertices with a given degree are Poissonian.

Mesoscopic fluctuations are significant in the large-degree region.

These fluctuations are crucial in networks with fat-tailed degree distributions.

Abstract

We describe fluctuations in finite-size networks with a complex distribution of connections, $P(k)$. We show that the spectrum of fluctuations of the number of vertices with a given degree is Poissonian. These mesoscopic fluctuations are strong in the large-degree region, where $P(k) \lesssim 1/N$ ($N$ is the total number of vertices in a network), and are important in networks with fat-tailed degree distributions.