Random networks with q-exponential degree distribution

TL;DR

This paper introduces a method to generate networks with a $q$-exponential degree distribution, analyzing their robustness, connectivity, and structural properties, revealing their potential as models for complex systems.

Contribution

It presents a novel network model with $q$-exponential degree distribution and analyzes its structural robustness and properties compared to scale-free networks.

Findings

$q$-exponential networks are more robust against failures and attacks.

They exhibit higher $k_s$-cores than scale-free networks.

These networks combine scale-free and small-world properties.

Abstract

We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the assortativity and the shortest path of these networks finding that the more the distribution resembles a pure power law, the less well connected are the corresponding nodes. In fact, the average degree of a nearest neighbor grows monotonically with $\lambda^{-1}$. Moreover, our results show that $q$-exponential networks are more robust against random failures and against malicious attacks than standard scale-free networks. Indeed, the critical fraction of removed nodes grows logarithmically with $\lambda^{-1}$ for malicious attacks. An analysis of the $k_s$-core decomposition shows that $q$-exponential networks have a highest $k_s$-core, that is bigger and has a larger $k_s$ than pure scale-free networks. Being at the same time well connected and robust, networks with $q$-exponential degree distribution exhibit scale-free and small-world properties, making them a particularly suitable model for application in several systems.