Community Detection in Degree-Corrected Block Models
This work addresses the problem of accurately partitioning network nodes into clusters for data analysts, representing an incremental improvement by focusing on degree-corrected models.
The paper tackles community detection in Degree-Corrected Block Models by deriving asymptotic minimax risks for misclassification proportion loss and proposing a polynomial-time algorithm for consistent and asymptotically optimal detection.
Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes, and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.