Strength Distribution in Derivative Networks

TL;DR

This paper introduces derivative complex networks where node weights depend on differences in assigned fitness values, revealing that their strength distribution follows a power law with an exponent depending on fitness bounds, with potential implications for neuronal networks.

Contribution

The paper presents an analytical and experimental study of derivative networks, showing how their strength distribution follows a power law with a specific exponent based on fitness limits, a novel insight.

Findings

Strength density follows a power law with exponent < 1 if fitness has an upper limit.

Strength density follows a power law with exponent > 1 if fitness has no upper limit but a positive lower limit.

Implications discussed for neuronal network topology and dynamics.

Abstract

This article describes a complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown both analytically and experimentally that the strength density (i.e. the weighted node degree) for this model, called derivative complex networks, follows a power law with exponent $\gamma<1$ if the fitness has an upper limit and $\gamma>1$ if the fitness has no upper limit but a positive lower limit. Possible implications for neuronal networks topology and dynamics are also discussed.