# Extended Scale-Free Networks

## TL;DR

This paper introduces the concept of extended scale-free networks, inspired by the extended Pareto distribution, providing a more realistic model for real-world networks that accounts for deviations from strict scale-free properties.

## Contribution

It proposes the extended scale-free network concept, addressing limitations of strict scale-free models and aligning with observations about sub-network properties.

## Key findings

- Extended scale-free networks better describe real networks.
- Sub-networks of scale-free networks are extended scale-free, not strictly scale-free.
- The model accounts for second- and third-order deviations.

## Abstract

Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the later, those sub-networks are asymptotically scale-free, but one should not forget about second-order deviation (possibly also third order actually). In this article, we introduce a concept of extended scale-free network, inspired by the extended Pareto distribution, that actually is maybe more realistic to describe real network than the strict scale free property. This property is consistent with Stumpf, Wiuf & May (2005): sub-network of scale-free larger networks are not strictly scale-free, but extended scale-free.