Existence of a persistent hub in the convex preferential attachment model
Probability
2016-12-30 v3
Abstract
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model with probability one. We also extend this result to the class of convex preferential attachment graphs, where a vertex of degree gets a new edge with probability proportional to some convex function of .
Keywords
Cite
@article{arxiv.1310.7513,
title = {Existence of a persistent hub in the convex preferential attachment model},
author = {Pavel Galashin},
journal= {arXiv preprint arXiv:1310.7513},
year = {2016}
}