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.
Original language | English |
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Pages (from-to) | 1159-1188 |
Number of pages | 30 |
Journal | Bernoulli |
Volume | 27 |
Issue number | 2 |
DOIs | |
Publication status | Published - May 2021 |
Bibliographical note
Funding Information:The work of RvdH was supported in part by the Netherlands Organisation for Scientific Research (NWO) through the Gravitation NETWORKS grant 024.002.003.
Publisher Copyright:
© 2021 ISI/BS
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
Keywords
- Community detection
- Inhomogeneous random graphs
- Minimax hypothesis testing
- Scan statistics