On the continuous-time limit of the Barab\'asi-Albert random graph

TL;DR

This paper demonstrates that the Barabási-Albert model converges to a set of generalized Yule models under proper scaling, providing a new perspective on its asymptotic properties through a novel limit process.

Contribution

It introduces a new limit process for the Barabási-Albert model by establishing its weak convergence to generalized Yule models, using a superimposed process and sampling procedure.

Findings

Barabási-Albert model converges to generalized Yule models

New limit process offers alternative analysis of asymptotic properties

Superimposed processes facilitate understanding of graph evolution

Abstract

We prove that the Barab\'asi-Albert model converges weakly to a set of generalized Yule models via an appropriate scaling. To pursue this aim we superimpose to its graph structure a suitable set of processes that we call the planted model and we introduce an ad-hoc sampling procedure. The use of the obtained limit process represents an alternative and advantageous way of looking at some of the asymptotic properties of the Barab\'asi-Albert random graph.