English

A Method for Generating Connected Erdos-Renyi Random Graphs

Data Structures and Algorithms 2025-10-21 v2 Discrete Mathematics Information Theory Combinatorics math.IT Probability

Abstract

We propose a novel exact algorithm for generating connected Erdos-Renyi random graphs G(n,p)G(n,p). The method couples the graph exploration process to an inhomogeneous Poisson random walk, which yields an exact sampler that runs in O(n)O(n) time in the sparse regime p=c/np=c/n. We also show how the method extends to the G(n,M)G(n,M) model via an additional acceptance-rejection step.

Keywords

Cite

@article{arxiv.2504.05907,
  title  = {A Method for Generating Connected Erdos-Renyi Random Graphs},
  author = {Boris Chinyaev},
  journal= {arXiv preprint arXiv:2504.05907},
  year   = {2025}
}
R2 v1 2026-06-28T22:50:41.060Z