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arXiv · 2602.05852

Exact Recovery in the Data Block Model

Amir R. Asadi·Akbar Davoodi·Ramin Javadi·Farzad Parvaresh
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Abstract

Community detection in networks is a fundamental problem in machine learning and statistical inference, with applications in social networks, biological systems, and communication networks. The stochastic block model (SBM) serves as a canonical framework for studying community structure, and exact recovery, identifying the true communities with high probability, is a central theoretical question. While classical results characterize the phase transition for exact recovery based solely on graph connectivity, many real-world networks contain additional data, such as node attributes or labels. In this work, we study exact recovery in the Data Block Model (DBM), an SBM augmented with node-associated data, as formalized by Asadi, Abbe, and Verd\'{u} (2017). We introduce the Chernoff--TV divergence and use it to characterize a sharp exact recovery threshold for the DBM. We further provide an efficient algorithm that achieves this threshold, along with a matching converse result showing impossibility below the threshold. Finally, simulations validate our findings and demonstrate the benefits of incorporating vertex data as side information in community detection.

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Amir R. Asadi, Akbar Davoodi, Ramin Javadi, Farzad Parvaresh. 2026-02-05. Exact Recovery in the Data Block Model. https://arxiv.org/abs/2602.05852

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