{
  "abstract": "Routing and search respond in opposite ways to rapid network expansion. Short graph distances make a known destination easy to reach, while the neighborhood accessible within a few hops can be vastly larger than any finite inspection budget. We show that this tension imposes an algorithm-independent constraint on sparse search. If $m_q$ relevant nodes are placed without structural information among $N$ nodes and at most $M$ nodes can be inspected, any target-blind exploration protocol has success probability at most $Mm_q/N$, irrespective of correlations between successive inspections, of revisits, and of any structural preference the exploration rule may have. Geometry determines when this constraint becomes relevant: a target becomes accessible with order-one probability when the graph-distance ball volume satisfies $V(R_c)\\sim N/m_q$. At this scale, any inspection mechanism achieving a fixed success probability $δ>0$ must enrich the probability of inspecting relevant nodes by at least order $N/(Mm_q)$ relative to the neutral target density. For uniformly searched candidate sets, this entails a vanishing visible fraction of the accessible region. Thus rapidly expanding networks can make rare targets geometrically close while target-blind search remains ineffective. Numerical results on Krioukov hyperbolic random graphs and two-dimensional lattices show that this separation can arise within only a few hops in the rapidly expanding case, while the lattice accessibility radius grows algebraically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31042",
  "author_total": 1,
  "authors": [
    {
      "name": "Antonio Scala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay6zkrsr35ppe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31042",
  "fulltext_url": null,
  "id": "ay6zkrsr35ppe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31042",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7214664619",
  "pdf_url": "https://arxiv.org/pdf/2609.31042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay6zkrsr35ppe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.31042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31042"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Reachability Does Not Imply Searchability in Expanding Networks",
  "title_text": "Reachability Does Not Imply Searchability in Expanding Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/ay6zkrsr35ppe",
  "venue": "arXiv",
  "versions": []
}