Analytic solution of a static scale-free network model

TL;DR

This paper provides an exact analytical solution for the Static Model of scale-free networks, revealing disassortative correlations caused by the absence of self and multiple connections, validated by simulations.

Contribution

It introduces a novel mapping to a hidden variables formalism and derives exact expressions for key properties of the scale-free network model.

Findings

Analytical expressions match simulation results in large networks.

Disassortative correlations are induced by connection constraints.

The mapping is exact in the infinite network size limit.

Abstract

We present a detailed analytical study of a paradigmatic scale-free network model, the Static Model. Analytical expressions for its main properties are derived by using the hidden variables formalism. We map the model into a canonic hidden variables one, and solve the latter. The good agreement between our predictions and extensive simulations of the original model suggests that the mapping is exact in the infinite network size limit. One of the most remarkable findings of this study is the presence of relevant disassortative correlations, which are induced by the physical condition of absence of self and multiple connections.