| dc.description.abstract | Network, or graph, represent relationships between entities in various applications, such as social networks, biological systems, and communication networks. A common feature in network data is the presence of community structures, where groups of nodes exhibit higher connectivity within themselves than with other groups. Identifying these community structures, a task known as community detection, is essential for gaining valuable insights in diverse applications, including uncovering hidden relationships in social networks, detecting functional modules in biological systems, and identifying vulnerabilities in communication networks. However, real-world network data may have missing values, significantly impacting the network’s structural properties. Existing community detection methods primarily focus on networks without missing values, leaving a gap in the analysis of censored networks. This study addresses the community detection problem in censored m-uniform hypergraphs. Firstly, utilizing an information-theoretic approach, we obtain a threshold that enables the exact recovery of the community structure. Then, we proposed a two-stage polynomial-time algorithm, which encompasses a spectral algorithm complemented by a refinement step, aiming to achieve exact recovery. Moreover, we introduce a semi-definite relaxation algorithm, studying its operational performance as a standalone community detection algorithm, without the integration of a refinement step. Lastly, in consideration of the effect of imputation methods on censored hypergraphs, we propose several methods grounded in network properties. We subsequently employ simulation to assess the performance of these methods. Finally, we apply the proposed algorithm to real-world data, showcasing its practical utility in various settings. | en_US |
