Generalised De-Preferential Random Graphs

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.