Testing Correlation in Graphs by Counting Bounded Degree Motifs

Dong Huang; Pengkun Yang

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arXiv · 2510.25289

Testing Correlation in Graphs by Counting Bounded Degree Motifs

Dong Huang·Pengkun Yang

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Abstract

We investigate the problem of detecting correlation between two Erd\H{o}s-R\'enyi graphs $G(n,p)$, formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent, while under the alternative hypothesis, they are correlated through a latent bijective mapping between their vertex sets. We develop a polynomial-time test by counting bounded degree motifs and prove its effectiveness for any constant correlation coefficient $\rho$ when the edge connecting probability satisfies $p\ge n^{-1+\delta}$ for some constant $\delta>0$. In particular, our guarantee improves the constrain of motif-counting methods from $\rho\ge \sqrt{\alpha}$ to any constant $\rho = \Omega(1)$, where $\alpha\approx 0.338$ is the Otter's constant.

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Dong Huang, Pengkun Yang. 2025-10-29. Testing Correlation in Graphs by Counting Bounded Degree Motifs. https://arxiv.org/abs/2510.25289

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