Assortativity in random line graphs

TL;DR

This paper studies degree correlations in various network types and shows that line graphs derived from these networks are generally assortative with positive degree correlations.

Contribution

It provides a theoretical and numerical analysis of degree correlations in line graphs, revealing their positive assortativity across different network models.

Findings

Exponential networks exhibit the strongest degree correlations.

Line graphs are consistently assortative with positive degree-degree correlation.

Theoretical and numerical results align in showing positive correlations in line graphs.

Abstract

We investigate the degree-degree correlations in the Erdos-Renyi networks, the growing exponential networks and the scale-free networks. We demonstrate that these correlations are the largest for the exponential networks. We calculate also these correlations in the line graphs, formed from the considered networks. Theoretical and numerical results indicate that all the line graphs are assortative, i.e. the degree-degree correlation is positive.