Discretization-free exact recovery in geometric community detection
Abstract
Geometric community detection seeks to recover latent communities in networks where connectivity depends jointly on community structure and continuous spatial geometry. Existing exact-recovery approaches typically discretize the underlying space, which can impose restrictive structural assumptions on the connectivity functions. We develop a polynomial-time, discretization-free algorithm for exact recovery in the Geometric Hidden Community Model (GHCM), operating directly on the continuous geometry. Our method succeeds even when connectivity functions coincide on a nontrivial portion of their visibility range and when two communities can be distinguished only through their connectivity to a third community. We prove exact recovery under these weaker conditions and provide experiments showing that the algorithm succeeds beyond the theoretically guaranteed regime.
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BibTeX
@misc{hoeneveld2026discretizationfree,
title = {{Discretization-free exact recovery in geometric community detection}},
author = {Maarten Hoeneveld and Moritz Otto and Raphaël Sala},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01635},
eprint = {2609.01635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01635},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discretization-free exact recovery in geometric community detection
AU - Maarten Hoeneveld
AU - Moritz Otto
AU - Raphaël Sala
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01635
UR - https://arxiv.org/abs/2609.01635
AB - Geometric community detection seeks to recover latent communities in networks where connectivity depends jointly on community structure and continuous spatial geometry. Existing exact-recovery approaches typically discretize the underlying space, which can impose restrictive structural assumptions on the connectivity functions. We develop a polynomial-time, discretization-free algorithm for exact recovery in the Geometric Hidden Community Model (GHCM), operating directly on the continuous geometry. Our method succeeds even when connectivity functions coincide on a nontrivial portion of their visibility range and when two communities can be distinguished only through their connectivity to a third community. We prove exact recovery under these weaker conditions and provide experiments showing that the algorithm succeeds beyond the theoretically guaranteed regime.
ER -