English

Rank-k random graphs and finite type branching processes

Probability 2022-07-26 v1 Combinatorics

Abstract

In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-kk random graphs}, and that are special in that their neighborhood explorations can be obtained by a {\em thinning} of multi-type branching processes. We show that any rank-2 random graph can be described in terms of thinning of a 2-type branching process, while for higher rank, it is not clear how many types are needed.

Keywords

Cite

@article{arxiv.2207.11471,
  title  = {Rank-k random graphs and finite type branching processes},
  author = {Suman Chakraborty and Kjell Raaijmakers and Remco van der Hofstad},
  journal= {arXiv preprint arXiv:2207.11471},
  year   = {2022}
}

Comments

12 pages

R2 v1 2026-06-25T01:10:04.028Z