Preferential attachment with choice based edge-step

TL;DR

This paper investigates how the maximum degree evolves in a preferential attachment model that incorporates a choice-based edge-step, revealing effects like condensation on multiple vertices with different types.

Contribution

It introduces a vertex type component into the model and analyzes the asymptotic behavior of the maximum degree, including phenomena like condensation.

Findings

Condensation occurs on multiple vertices with different types.

The maximum degree exhibits specific asymptotic behavior.

Vertex types influence the degree distribution dynamics.

Abstract

We study the asymptotic behavior of the maximum degree in the preferential attachment model with a choice-based edge-step. We add vertex type to the model and prove, among others types of behavior, the effect of condensation on multiple vertices with different types.