Reconstruction of evolved dynamic networks from degree correlations

TL;DR

This paper investigates how local structural properties like degree correlations influence the spectral scaling of evolved networks, revealing that two-point correlations are crucial for reproducing power-law spectral behavior.

Contribution

It demonstrates that degree correlations, especially two-point correlations, are essential for replicating the spectral properties of evolved networks, beyond just degree distribution and clustering.

Findings

Degree distribution alone does not reproduce spectral scaling.

Degree-dependent clustering has an indirect effect.

Two-point degree correlations are key to spectral power-law scaling.

Abstract

We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent clustering are extracted from the evolved networks and used to construct random networks with the prescribed distributions. In the analysis of these reconstructed networks it turns out that the degree distribution alone is not sufficient to generate the spectral scaling and the degree-dependent clustering has only an indirect influence. The two-point correlations are found to be the dominant characteristic for the power-law scaling over a broader eigenvalue range.