Are Barabasi-Albert networks self-averaging?

TL;DR

This paper investigates the self-averaging properties of Barabasi-Albert networks, showing that some features fluctuate significantly while others become more stable as the network size grows.

Contribution

It provides a nuanced analysis of which network properties in Barabasi-Albert models are self-averaging and how fluctuations behave with increasing network size.

Findings

Largest neighborhood size fluctuates with network size

Number of nodes with exactly ten neighbors increases linearly

Relative fluctuations decrease as network size grows

Abstract

Yes and no. The size of the largest neighbourhood in a Barabasi-Albert scale-free entwork has string fluctuations of the order of the average value. The number of sites having exactly ten neighbours increases linearly in the network size while its relative fluctuations decrease towards zero if the number of sites in the network increases from 1000 to ten million.