The phase transition in Chung-Lu graphs
Probability
2023-05-16 v1
Abstract
In 2002, Chung and Lu introduced a version of the Erdos-Renyi model which an edge between and is present with probability . They applied this model to compute the diameter of power-law random graphs, with yielded easier proofs than those for the configuration model. In 2007 their model was brought and integrated under the umbrella of Bolobas, Janson, and Riordan's inhomogeneous random graphs. However, the properties of the Chung-Lu model were never fully explored. In this paper, we fill the gap by giving a result for the cluster sizes in the subcritical regime and the fraction of vertices in the giant component in the supercritical phase.
Keywords
Cite
@article{arxiv.2305.08203,
title = {The phase transition in Chung-Lu graphs},
author = {Aolan Ding and Rick Durrett},
journal= {arXiv preprint arXiv:2305.08203},
year = {2023}
}