Preferential attachment random graphs with edge-step functions

In this talk we will discuss our recent work introducing a model of preferential attachment random graphs where the asymptotic ratio between vertices and edges of the graph is governed by a non-increasing regularly varying function $f:\mathbb{N}\to [0,1]$, which we call the edge-step function. We prove general results about the associated empirical degree distribution, as well as topological results about the clique number and the diameter. Joint work with Rémy Sanchis and Rodrigo Ribeiro.