Further properties of a random graph with duplications and deletions

TL;DR

This paper investigates a random graph model involving vertex duplication and edge deletion, analyzing degree distributions, asymptotic bounds, and phase transitions based on duplication and deletion probabilities.

Contribution

It provides new insights into the limit distribution of vertex degrees and phase transition phenomena in a graph model with duplication and deletion processes.

Findings

Limit distribution of vertex degree analyzed

Asymptotic bounds for maximal degree established

Phase transition identified based on duplication and deletion probabilities

Abstract

We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a fixed vertex, and derive a.s. asymptotic bounds for the maximal degree. The model shows a phase transition phenomenon with respect to the probabilities of duplication and deletion.