Efficiency of Scale-Free Networks: Error and Attack Tolerance

TL;DR

This paper investigates how scale-free networks respond to errors and attacks, revealing they are highly tolerant to random failures but extremely vulnerable to targeted attacks, using efficiency measures.

Contribution

It introduces the use of global and local efficiency to analyze error and attack tolerance in different types of scale-free networks.

Findings

Scale-free networks are error tolerant on a global and local scale.

They are highly vulnerable to targeted removal of key nodes.

Global efficiency better describes network response than characteristic path length.

Abstract

The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e. networks with power law P(k), are considered: 1) scale-free networks with no local clustering produced by the Barabasi-Albert model and 2) scale-free networks with high clustering properties as in the model by Klemm and Eguiluz, and their properties are compared to the properties of random graphs (exponential graphs). By using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network. We show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors. We find that, at variance with random graphs, scale-free networks display, both on a global and on a local scale, a high degree of error tolerance and an extreme vulnerability to attacks. In fact, the global and the local efficiency are unaffected by the failure of some randomly chosen nodes, though they are extremely sensititive to the removal of the few nodes which play a crucial role in maintaining the network's connectivity.