2020/04/30 by Lihua Lei, Xiaodong Li, Lei, Lihua +3
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Advanced Graph Neural Networks #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2004.14531
openalex publication_date 2020/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is dividing the network into two communities based on the Fiedler vector of the unnormalized graph Laplacian and repeating the split until a stopping rule indicates no further community structures. We prove the strong consistency of this method under a wide range of model parameters, which include sparse networks with node degrees as small as O(log n). In addition, unlike most of existing work, our theory covers multiscale networks where the connection probabilities may differ by orders of magnitude, which comprise an important class of models that are practically relevant but technically challenging to deal with. Finally we demonstrate the performance of our algorithm on synthetic data and real-world examples.