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arXiv · 2504.05907

A Method for Generating Connected Erdos-Renyi Random Graphs

Boris Chinyaev
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Abstract

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

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Boris Chinyaev. 2025-04-08. A Method for Generating Connected Erdos-Renyi Random Graphs. https://arxiv.org/abs/2504.05907

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