Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding
This solves the problem of community detection in network analysis for researchers and practitioners, offering a rigorous foundation for clustering methods.
The paper proves that adjacency spectral embedding achieves perfect clustering for stochastic blockmodel graphs and its variants, providing a theoretical guarantee for exact community detection.
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We also show an analogous result for the more general random dot product graph model.