# Community Detection and Classification in Hierarchical Stochastic Blockmodels

arXiv: https://arxiv.org/abs/1503.02115 · HTML: https://mlsanity.com/paper/1503.02115/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2015.

## Built on by (most cited first, 23 of 23)

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- [When Does Bottom-up Beat Top-down in Hierarchical Community Detection?](https://mlsanity.com/paper/2306.00833/) (2023)
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- [Adversarial contamination of networks in the setting of vertex nomination: a new trimming method](https://mlsanity.com/paper/2208.09710/) (2022)
- [Dynamic Network Sampling for Community Detection](https://mlsanity.com/paper/2208.13921/) (2022)
- [Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings](https://mlsanity.com/paper/2409.17544/) (2024)
- [Matching and mixing: Matchability of graphs under Markovian error](https://mlsanity.com/paper/2601.20020/) (2026)
- [Adjacency Spectral Embeddings of Correlation Networks](https://mlsanity.com/paper/2602.21055/) (2026)
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## Abstract (arXiv)

We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Euclidean space to obtain a low-dimensional representation, and then cluster the vertices into communities. We next employ nonparametric graph inference techniques to identify structural similarity among these communities. These two steps are then applied recursively on the communities, allowing us to detect more fine-grained structure. We describe a hierarchical stochastic blockmodel---namely, a stochastic blockmodel with a natural hierarchical structure---and establish conditions under which our algorithm yields consistent estimates of model parameters and motifs, which we define to be stochastically similar groups of subgraphs. Finally, we demonstrate the effectiveness of our algorithm in both simulated and real data. Specifically, we address the problem of locating similar subcommunities in a partially reconstructed Drosophila connectome and in the social network Friendster.