Avalanche dynamics driven by adaptive rewirings in complex networks

TL;DR

This paper presents a toy model of failure cascades in scale-free networks with adaptive rewiring, revealing self-organized criticality and power-law avalanche size distributions.

Contribution

It introduces a novel model combining network growth, failure, and adaptive rewiring, demonstrating critical avalanche behavior and analyzing system breakdown times.

Findings

Avalanche size distribution follows a power law with exponent ~2.6.

System breakdown time depends on node capacity and is characterized statistically.

Rewiring can trigger successive failures leading to critical cascades.

Abstract

We introduce a toy model displaying the avalanche dynamics of failure in scale-free networks. In the model, the network growth is based on the Barab\'asi and Albert model and each node is assigned a capacity or tolerance, which is constant irrespective of node index. The degree of each node increases over time. When the degree of a node exceeds its capacity, it fails and each link connected to it is is rewired to other unconnected nodes by following the preferential attachment rule. Such a rewiring edge may trigger another failure. This dynamic process can occur successively, and it exhibits a self-organized critical behavior in which the avalanche size distribution follows a power law. The associated exponent is $\tau \approx 2.6(1)$. The entire system breaks down when any rewired edges cannot locate target nodes: the time at which this occurs is referred to as the breaking time. We obtain the breaking time as a function of the capacity. Moreover, using extreme value statistics, we determine the distribution function of the breaking time.