Detecting a planted community in an inhomogeneous random graph

Kay Bogerd, Rui M. Castro, Remco van der Hofstad, Nicolas Verzelen

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

6 Citaten (Scopus)

Samenvatting

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.

Originele taal-2Engels
Pagina's (van-tot)1159-1188
Aantal pagina's30
TijdschriftBernoulli
Volume27
Nummer van het tijdschrift2
DOI's
StatusGepubliceerd - mei 2021

Bibliografische nota

Publisher Copyright:
© 2021 ISI/BS

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

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