The distribution of second degrees in the Bollob\'as--Riordan random graph model

TL;DR

This paper proves that in the Bollobás--Riordan random graph model with parameter m=1, the distribution of second degrees follows a power law, revealing a specific structural property of the network.

Contribution

It establishes that the second degree distribution in this particular random graph model adheres to a power law, a result not previously demonstrated for this model.

Findings

Second degree distribution follows a power law

Results apply specifically to the case m=1

Enhances understanding of network structure in Bollobás--Riordan model

Abstract

We prove that the distribution of second degrees in the Bollob\'as--Riordan random graph model obeys the power law. We consider the model with parameter m = 1 (the number of edges equals the number of nodes).