Optimization of Robustness of Complex Networks

TL;DR

This paper investigates how to design complex networks that are robust against both random failures and targeted attacks, identifying optimal degree distributions that maximize resilience while maintaining constant average connectivity.

Contribution

It introduces network design guidelines for maximizing robustness to failures and attacks across various degree distribution types, including scale-free and multi-peak networks.

Findings

Optimal networks have most nodes with degree close to the average

One highly connected node with degree proportional to N^{2/3} enhances robustness

Designs balance resilience to different failure modes effectively

Abstract

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random failure and intentional attack while keeping the cost of the network (which we take to be the average number of links per node) constant. We find optimal parameters for: (i) scale free networks having degree distributions with a single power-law regime, (ii) networks having degree distributions with two power-law regimes, and (iii) networks described by degree distributions containing two peaks. Of these various kinds of distributions we find that the optimal network design is one in which all but one of the nodes have the same degree, $k_1$ (close to the average number of links per node), and one node is of very large degree, $k_2 \sim N^{2/3}$, where $N$ is the number of nodes in the network.