Robustness of the avalanche dynamics in data packet transport on scale-free networks

TL;DR

This paper investigates how avalanche sizes in data packet transport on scale-free networks follow a power-law distribution at a critical point, revealing robustness of the critical exponent across different network degree exponents.

Contribution

It introduces a simple model showing the critical behavior of avalanche dynamics and demonstrates the robustness of the critical exponent in scale-free networks.

Findings

Avalanche size distribution follows a power law at a critical parameter value.

The critical exponent remains robust for degree exponents between 2 and 3.

The exponent is similar to that of diameter changes caused by vertex removal.

Abstract

We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter $a$ as well as which vertex triggers it. We find that there exists a critical value $a_c$ at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3, and is close in value to that of the distribution of the diameter changes by single vertex removal.