Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat loose, network clusters or groups are generally considered as nodes with enriched interactions and edges sharing common patterns. Statistical inference often treats groups as latent variables, with observed networks generated from latent group structure, termed a stochastic block model. Regardless of the definitions, statistical inference can be either translated to modularity maximization, which is provably an NP-complete problem. Here we present scalable and reliable algorithms that recover hierarchical stochastic block models fast and accurately. Our algorithm scales almost linearly in number of edges, and inferred models were more accurate that other scalable methods.
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