# A measure for characterizing heavy-tailed networks

## TL;DR

The paper introduces the Cooke-Nieboer index (CNI), a simple, non-asymptotic measure to characterize the heavy-tailedness of networks' degree distributions, regardless of whether they follow a power law.

## Contribution

It proposes the CNI as a novel, easy-to-calculate metric that distinguishes between different types of degree distributions in networks.

## Key findings

- CNI effectively differentiates power-law, exponential, and symmetric distributions.
- CNI does not assume a specific distribution form, unlike traditional methods.
- The measure is applicable to real-world networks with diverse degree distributions.

## Abstract

Heavy-tailed networks are often characterized in the literature by their degree distribution's similarity to a power law. However, many heavy-tailed networks in real life do not have power-law degree distributions, and in many applications the scale-free nature of the network is irrelevant so long as the network possesses hubs. Here we present the Cooke-Nieboer index (CNI), a non-asymptotic measure of the heavy-tailedness of a network's degree distribution which does not presume a power-law form. The CNI is easy to calculate, and clearly distinguishes between networks with power-law, exponential, and symmetric degree distributions.