Clarifying How Degree Entropies and Degree-Degree Correlations Relate to Network Robustness

Area of Science:

• Network Science
• Complex Systems Analysis
• Information Theory

Background:

• The entropy of a network's degree distribution is frequently cited as a measure of its robustness to node removal.
• Existing research often assumes a direct correlation between degree distribution entropy and network resilience.
• However, the precise relationship and its limitations in various network configurations remain unclear.

Purpose of the Study:

• To clarify the relationship between degree distribution entropy and giant component robustness in networks.
• To investigate the predictive power of degree distribution entropy for network robustness under node removal.
• To explore alternative entropy measures and network characteristics that better indicate robustness.

Main Methods:

• Analysis of randomly configured networks to establish bounds for robustness based on degree distribution entropy.
• Comparative study of networks with fixed expected degrees and identical distribution forms to assess entropy's predictive value.
• Investigation of the relationship between remaining degree entropy and network robustness, including deriving analytic expressions for specific distributions (e.g., log-normal).
• Examination of degree-degree correlations and their impact on robustness in real-world networks.
• Proposal of an adjusted mutual information measure to better capture robustness-related structural properties.

Main Results:

• Degree distribution entropy provides only a lower bound for giant component robustness in random networks without further specifications.
• For networks with the same distribution form and fixed expected degree, degree distribution entropy does not reliably indicate robustness.
• A positive monotonic relationship exists between remaining degree entropy and network robustness.
• Degree-degree correlations alone are insufficient indicators of robustness in real networks.
• An adjusted mutual information measure is proposed to better reflect structural properties linked to robustness.

Conclusions:

• Degree distribution entropy is a limited proxy for network robustness, especially in random networks or those with similar degree distribution forms.
• Remaining degree entropy emerges as a more reliable indicator of network robustness to node removal.
• Further research should consider remaining degree entropy and refined mutual information measures for assessing network resilience.