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May 2021 Detecting a planted community in an inhomogeneous random graph
Kay Bogerd, Rui M. Castro, Remco van der Hofstad, Nicolas Verzelen
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Bernoulli 27(2): 1159-1188 (May 2021). DOI: 10.3150/20-BEJ1269

Abstract

We study the problem of detecting whether an inhomogeneous random graph contains a planted community. Specifically, we observe a single realization of a graph. Under the null hypothesis, this graph is a sample from an inhomogeneous random graph, whereas under the alternative, there exists a small subgraph where the edge probabilities are increased by a multiplicative scaling factor. We present a scan test that is able to detect the presence of such a planted community, even when this community is very small and the underlying graph is inhomogeneous. We also derive an information theoretic lower bound for this problem which shows that in some regimes the scan test is almost asymptotically optimal. We illustrate our results through examples and numerical experiments.

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Kay Bogerd. Rui M. Castro. Remco van der Hofstad. Nicolas Verzelen. "Detecting a planted community in an inhomogeneous random graph." Bernoulli 27 (2) 1159 - 1188, May 2021. https://doi.org/10.3150/20-BEJ1269

Information

Received: 1 October 2019; Revised: 1 August 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1269

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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