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arXiv · 2209.07554

Detecting Planted Partition in Sparse Multi-Layer Networks

Anirban Chatterjee·Sagnik Nandy·Ritwik Sadhu
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Abstract

Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multi-layer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network is greater than $1$. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provide a quasi-polynomial time algorithm to estimate it.

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Anirban Chatterjee, Sagnik Nandy, Ritwik Sadhu. 2024-05-24. Detecting Planted Partition in Sparse Multi-Layer Networks. https://arxiv.org/abs/2209.07554

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