Scale-Free Networks with the Same Degree Distribution: Different Structural Properties

TL;DR

This study compares structural properties of scale-free networks generated by different algorithms, revealing that identical degree distributions can lead to diverse network topologies with significant implications for dynamic processes.

Contribution

It demonstrates that networks with the same degree distribution can have markedly different structural properties depending on the generation algorithm used.

Findings

Model B produces decentralized networks with many components.

BA networks are centralized with a single giant component.

Structural differences affect dynamics on the networks.

Abstract

We have analysed some structural properties of scale-free networks with the same degree distribution. Departing from a degree distribution obtained from the Barab\'asi-Albert (BA) algorithm, networks were generated using four additional different algorithms a (Molloy-Reed, Kalisky, and two new models named A and B) besides the BA algorithm itself. For each network, we have calculated the following structural measures: average degree of the nearest neighbours, central point dominance, clustering coefficient, the Pearson correlation coefficient, and global efficiency. We found that different networks with the same degree distribution may have distinct structural properties. In particular, model B generates decentralized networks with a larger number of components, a smaller giant component size, and a low global efficiency when compared to the other algorithms, especially compared to the centralized BA networks that have all vertices in a single component, with a medium to high global efficiency. The other three models generate networks with intermediate characteristics between B and BA models. A consequence of this finding is that the dynamics of different phenomena on these networks may differ considerably.