{
  "abstract": "We study the inference of a planted dense component in a sparse random graph from a single spreading process. The graph has an Erdős-Rényi background with edge probability $p_n$ and contains a planted dense component of size $n^α$, with $α> 1/2$, whose internal edge density $ξ>0$ is constant. The edge set is unobserved; the data only consist of the successive infection times from a single realization of a continuous-time SI process with independent and exponentially distributed transmission times. We show that the planted dense component leaves a detectable signature in the spreading process: after the exploration enters the dense component, it undergoes a short phase of accelerated growth. By analyzing this phase, we localize its onset and endpoint. These localization results yield consistent estimators of the component-size exponent $α$, the background edge density $p_n$, and the internal edge density $ξ$ from the infection times alone. When the identities of the infected vertices are also observed, we further establish consistent recovery of the planted dense component.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08766",
  "author_total": 3,
  "authors": [
    {
      "name": "Maximilien Dreveton"
    },
    {
      "name": "Paula Mürmann"
    },
    {
      "name": "Patrick Thiran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p3gp8whk1fq9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08766",
  "fulltext_url": null,
  "id": "9p3gp8whk1fq9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08766",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7220921321",
  "pdf_url": "https://arxiv.org/pdf/2610.08766",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p3gp8whk1fq9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08766",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08766"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Estimation and Recovery of a Planted Dense Subgraph from a Single Network Cascade",
  "title_text": "Estimation and Recovery of a Planted Dense Subgraph from a Single Network Cascade",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/9p3gp8whk1fq9",
  "venue": "arXiv",
  "versions": []
}