Degree-correlation, robustness, and vulnerability in finite scale-free networks

TL;DR

This paper investigates how degree correlation affects the robustness and vulnerability of finite scale-free networks, revealing that positive correlation enhances robustness but increases vulnerability to random node deletion.

Contribution

It specifically analyzes the impact of degree correlation on network robustness and vulnerability, extending prior work focused mainly on degree distribution.

Findings

Positive degree-correlation increases network robustness.

Networks with positive correlation are more vulnerable to random node deletion.

Targeted deletion effectiveness depends on topology changes.

Abstract

Many naturally occurring networks have a power-law degree distribution as well as a non-zero degree correlation. Despite this, most studies analyzing the robustness to random node-deletion and vulnerability to targeted node-deletion have concentrated only on power-law degree distribution and ignored degree correlation. This study looks specifically at the effect degree-correlation has on robustness and vulnerability in scale-free networks. Our results confirm Newman's finding that positive degree-correlation increases robustness and decreases vulnerability. However, we found that networks with positive degree-correlation are more vulnerable to random node-deletion than to targeted deletion methods that utilize knowledge of initial node-degree only. Targeted deletion sufficiently alters the topology of the network to render this method less effective than uniform random methods unless changes in topology are accounted for. This result indicates the importance of degree correlation in certain network applications.