A Scale-free Network with Boolean Dynamics as a Function of Connectivity

TL;DR

This paper investigates how Boolean dynamics on scale-free networks with varying degree distributions exhibit power-law behaviors in damage spreading, with exponents influenced by the network's degree distribution exponent.

Contribution

It introduces a model of Boolean dynamics on scale-free networks using simple logical functions and analyzes how damage spreading depends on network connectivity and degree distribution.

Findings

Hamming distance shows power-law dependence on parameter q

Number of 1's exhibits power-law behavior with q

Exponents depend on the degree distribution exponent er

Abstract

In this work we analyze scale-free networks with different power law spectra $N(k) \sim k^{-\gamma}$ under a boolean dynamic, where the boolean rule that each node obeys is a function of its connectivity $k$. This is done by using only two logical functions (AND and XOR) which are controlled by a parameter $q$. Using damage spreading technique we show that the Hamming distance and the number of 1's exhibit power law behavior as a function of $q$. The exponents appearing in the power laws depend on the value of $\gamma$.