Entropy Optimization of Scale-Free Networks Robustness to Random Failures

TL;DR

This paper explores how maximizing the entropy of degree distributions in scale-free networks enhances their robustness to random failures, providing a method for optimal network design based on heterogeneity.

Contribution

It introduces entropy maximization as a novel approach to optimize the robustness of scale-free networks against random failures.

Findings

Entropy correlates with network resilience.

Optimal network design involves tuning the degree distribution.

Maximized entropy improves robustness to failures.

Abstract

Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free network robustness to random failures with average connectivity constant is equivalent to maximize the entropy of the degree distribution. By examining the relationship of entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free network to random failures. We conclude that entropy of the degree distribution is an effective measure of network's resilience to random failures.