Optimization of network structure to random failures

TL;DR

This paper uses a global optimization method to design network structures that maximize efficiency and resilience to random failures, revealing that highly heterogeneous networks with few hubs are most robust.

Contribution

It introduces a novel optimization approach for network design, identifying structural features that enhance robustness and efficiency under cost constraints.

Findings

Optimal networks are highly heterogeneous with few hubs and high clustering.

Higher efficiency correlates with increased robustness to random failures.

A simple model describes the statistical properties of optimal networks.

Abstract

Network's resilience to the malfunction of its components has been of great concern. The goal of this work is to determine the network design guidelines, which maximizes the network efficiency while keeping the cost of the network (that is the average connectivity) constant. With a global optimization method, memory tabu search (MTS), we get the optimal network structure with the approximately best efficiency. We analyze the statistical characters of the network and find that a network with a small quantity of hub nodes, high degree of clustering may be much more resilient to perturbations than a random network and the optimal network is one kind of highly heterogeneous networks. The results strongly suggest that networks with higher efficiency are more robust to random failures. In addition, we propose a simple model to describe the statistical properties of the optimal network and investigate the synchronizability of this model.