Parameters Affecting the Resilience of Scale-Free Networks to Random Failures

TL;DR

This paper challenges the common belief that scale-free networks are highly robust to random failures, showing that finite power-law networks, including Internet-like networks, are vulnerable to large-scale random node deletions, especially beyond certain failure thresholds.

Contribution

The study provides new analytical and empirical evidence that finite scale-free networks with minimum degree 1 are not as robust as previously thought, especially under high random failure rates.

Findings

Power-law networks lose connectivity rapidly beyond 0.9 failure probability.

Approximately 25% of nodes remain connected after 50% random node deletion.

Analytical model accounts for degree-0 nodes after failures.

Abstract

It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet. Their results suggest that if each node in this network failed independently with probability 0.99, the remaining network would continue to have a giant component. In this paper, we show that a large and important subclass of scale-free networks are not robust to massive numbers of random node deletions for practical purposes. In particular, we study finite scale-free networks which have minimum node degree of 1 and a power-law degree distribution beginning with nodes of degree 1 (power-law networks). We show that, in a power-law network approximating the Internet's reported distribution, when the probability of deletion of each node is 0.5 only about 25% of the surviving nodes in the network remain connected in a giant component, and the giant component does not persist beyond a critical failure rate of 0.9. The new result is partially due to improved analytical accommodation of the large number of degree-0 nodes that result after node deletions. Our results apply to finite power-law networks with a wide range of power-law exponents, including Internet-like networks. We give both analytical and empirical evidence that such networks are not generally robust to massive random node deletions.