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arXiv · 2203.14573

Detection threshold for correlated Erdős-Rényi graphs via densest subgraphs

Jian Ding·Hang Du
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Abstract

The problem of detecting edge correlation between two Erdős-Rényi random graphs on $n$ unlabeled nodes can be formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are sampled independently; under the alternative, the two graphs are independently sub-sampled from a parent graph which is Erdős-Rényi $\mathbf{G}(n, p)$ (so that their marginal distributions are the same as the null). We establish a sharp information-theoretic threshold when $p = n^{-α+o(1)}$ for $α\in (0, 1]$ which sharpens a constant factor in a recent work by Wu, Xu and Yu. A key novelty in our work is an interesting connection between the detection problem and the densest subgraph of an Erdős-Rényi graph.

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Jian Ding, Hang Du. 2022-05-29. Detection threshold for correlated Erdős-Rényi graphs via densest subgraphs. https://arxiv.org/abs/2203.14573

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