mlsanityData to 7 Oct 2026

Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding

arXiv 1310.0532 ↗First posted 2 Oct 2013stat.MLcited by 23

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Abstract (arXiv)

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.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Oct 2013.

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Citing papers per year: 2021: 7; 2022: 8; 2023: 2; 2024: 1; 2025: 3; 2026: 2.

23 papers.

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  1. 2021Spectral embedding for dynamic networks with stability guaranteescited by 13
  2. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  3. 2021Spectral clustering under degree heterogeneity: a case for the random walk Laplaciancited by 6
  4. 2021Matrix factorisation and the interpretation of geodesic distancecited by 6
  5. 2021Inducing a hierarchy for multi-class classification problemscited by 5
  6. 2021Hypothesis Testing for Equality of Latent Positions in Random Graphscited by 5
  7. 2022Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labelscited by 3
  8. 2021Exact Recovery of Community Structures Using DeepWalk and Node2veccited by 2
  9. 2023Consistency of Lloyd's Algorithm Under Perturbationscited by 2
  10. 2023Detection of Model-based Planted Pseudo-cliques in Random Dot Product Graphs by the Adjacency Spectral Embedding and the Graph Encoder Embeddingcited by 1
  11. 2021Latent structure blockmodels for Bayesian spectral graph clusteringcited by 0
  12. 2022Spectral embedding and the latent geometry of multipartite networkscited by 0
11 more
  1. 2022Perfect Spectral Clustering with Discrete Covariatescited by 0
  2. 2022Probability density estimation for sets of large graphs with respect to spectral information using stochastic block modelscited by 0
  3. 2022Adversarial contamination of networks in the setting of vertex nomination: a new trimming methodcited by 0
  4. 2022Dynamic Network Sampling for Community Detectioncited by 0
  5. 2022Learning Coherent Clusters in Weakly-Connected Network Systemscited by 0
  6. 2024Entrywise error bounds for low-rank approximations of kernel matricescited by 0
  7. 2025Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacycited by 0
  8. 2025Asymptotically perfect seeded graph matching without edge correlation (and applications to inference)cited by 0
  9. 2025Nonparametric learning of heterogeneous graphical model on network-linked datacited by 0
  10. 2026Adjacency Spectral Embeddings of Correlation Networkscited by 0
  11. 2026Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embeddingcited by 0