On dynamic random graphs with degree homogenization via anti-preferential attachment probabilities

TL;DR

This paper studies a dynamic random graph model combining preferential and anti-preferential attachment, deriving degree distributions and analyzing how degree homogenization influences convergence and distribution properties.

Contribution

It introduces a mixed attachment model and provides asymptotic degree distribution results, highlighting the effects of degree homogenization on convergence and distribution.

Findings

Derived asymptotic degree distribution for the model

Analyzed the impact of degree homogenization on convergence rates

Studied the degree process in pure anti-preferential attachment case

Abstract

We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a preferential attachment mechanism. We derive the asymptotic degree distribution in the general case and study the asymptotic behaviour of the expected degree process in the general and that of the degree process in the pure anti-preferential attachment case. Degree homogenization mainly affects convergence rates for the former case and also the limiting degree distribution in the latter.