Growing Scale-free Networks by a Mediation-Driven Attachment Rule

TL;DR

This paper introduces a new network growth model where nodes connect via a mediation-driven rule, resulting in power-law degree distributions with variable exponents and unique attachment dynamics.

Contribution

The model demonstrates a novel mediation-driven attachment mechanism that produces power-law networks with tunable exponents and reveals new phenomena like super-preferential attachment.

Findings

Power-law degree distributions with variable exponents depending on m.

Identification of a mediation-driven attachment process leading to super-preferential attachment.

A measure based on the inverse harmonic mean characterizes the degree distribution's shape.

Abstract

We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the Barab\'{a}si-Albert (BA) model, each new node first picks an existing node at random, and connects not with this but with $m$ of its neighbors also picked at random. Counterintuitively enough, such a mediation-driven attachment rule results not only in preferential but super-preferential attachment, albeit in disguise. We show that for small $m$, the dynamics of our model is governed by winners take all phenomenon, and for higher $m$ it is governed by winners take some. Besides, we show that the mean of the inverse harmonic mean of degrees of the neighborhood of all existing nodes is a measure that can well qualify how straight the degree distribution is.