What exactly are the properties of scale-free and other networks?

TL;DR

This paper provides tools to analyze network properties, revealing the true characteristics of scale-free networks and questioning some previously claimed features attributed to them.

Contribution

It introduces methods for analyzing networks with arbitrary degree distributions, clarifying the actual properties of scale-free networks and challenging prior assumptions.

Findings

Scale-free networks have specific, often misunderstood properties.

Some claimed properties of scale-free networks are not intrinsic.

The paper offers new tools for rigorous network analysis.

Abstract

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly likely properties, and some unrecognised richness, of scale-free networks, and casts doubt on some previously claimed properties being due to a scale-free characteristic.