Generalised De-Preferential Random Graphs

TL;DR

This paper extends the analysis of generalized random graph models, providing asymptotic degree distributions and showing how different inverse power law cases affect the growth of vertex degrees.

Contribution

It introduces new asymptotic results for generalized de-preferential random graphs, especially highlighting differences in degree growth under inverse power law and linear cases.

Findings

Asymptotic degree of fixed vertices derived

Degree distribution characterized for generalized models

Inverse power law cases grow slower than simple inverse functions

Abstract

We consider some further generalizations of the novel random graph models as introduced by Bandyopadhyay and Sen \cite{BaSe2025} and find asymptotic for the degree of a fixed vertex and along with the asymptotic degree distribution. We show that in the \emph{case of the inverse power law} the order of these statistics is much slower than the case of the simple inverse function, which was considered in \cite{BaSe2025}. However, the results for the linear case remain exactly the same even after introducing a "shift" parameter.