Phase transition in preferential attachment-detachment through embedding

TL;DR

This paper investigates a random graph model with preferential attachment and detachment, revealing phase transitions in degree distribution behavior across different parameter regimes.

Contribution

It introduces a generalized Yule model for preferential attachment-detachment and characterizes the degree distribution's phase transition behavior.

Findings

Power law degree distribution in supercritical regime

Exponential decay in subcritical regime

Intermediate decay at critical regime

Abstract

We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the supercritical regime but has an exponential decay in the subcritical. We provide the corresponding asymptotics. In the critical regime we observe an intermediate decay. The regimes are clearly defined in terms of parameter ranges.