{
  "abstract": "Aggregated relational data replaces a fully observed network with a compressed version, where survey respondents are asked questions such as ``How many of your friends belong to group $G$?''. We consequently only observe a matrix $R = OA$ of the adjacency matrix $A$ with a fixed design $O$. In this paper we understand the effects of this compression on community detection under degree-corrected stochastic block models. First, we give guarantees for when it is possible to recover the full network parameters, and then only just the communities under conditions on a diagonal corrected version of $\\mathbb{E}[R]$, which can be used to inform experimental design. Secondly, we show that spectral clustering with single linkage exactly recovers communities when $nρ_n\\gtrsim K^2+K\\log n$ when there are $K$ balanced communities under ``uniformly spread'' or near-orthogonal designs, and characterize more generally how the design influences rates of convergence. We also introduce second-order ``friends-of-friends'' queries and develop the corresponding theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03937",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrew Davison"
    },
    {
      "name": "Owen G. Ward"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3gnqz69yhyf3k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03937",
  "fulltext_url": null,
  "id": "3gnqz69yhyf3k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03937",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7220692750",
  "pdf_url": "https://arxiv.org/pdf/2610.03937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3gnqz69yhyf3k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.03937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Community Detection from Aggregated Relational Data: Identifiability and Spectral Recovery",
  "title_text": "Community Detection from Aggregated Relational Data: Identifiability and Spectral Recovery",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/3gnqz69yhyf3k",
  "venue": "arXiv",
  "versions": []
}