{
  "abstract": "Motif profiles of bipartite agent-object networks, such as tourist-site visits and customer-item transactions, are read as evidence about structural roles and about differences between networks, often without asking what the two degree sequences already fix. In a simple bipartite graph the induced k-fan count on one node type is a sum of degree combinations, so it has zero variance under a null that preserves both degree sequences. We apply this known result to a reconstructed tourism rating network of 17 tourists, 80 sites and 637 edges, the sole inferential worked example, and, as a provenance-limited illustration, to published motif-instance aggregates over 36 monthly luxury customer-item networks. The four fan classes are exact functions of the degree sequences: in the tourism network the raw fan counts and the size-3 two-fan ratio (84.7% fan-out) restate those sequences. The published luxury counts require at least 89,502 customer-item edges against 26,451 reported transactions, so their 99.8% fan-in is reported as a descriptive value only. Against a hard bipartite configuration null, the four-cycle count is degree-consistent (z about +1.0) and the open path is deficient (z about -5.8) by 2,243 instances, 2.4% of the null mean; the deficit survives every leave-one-tourist-out re-run (z -4.5 to -8.1). An exact identity splits it at the point estimate into 64.4% mixing and 35.6% four-cycle, but that split is not an attribution: the observed mixing term lies below all 500 null samples, the two components are almost collinear under the null (r = 0.968), and the mixing share ranges from 36.6% to 116.5% under leave-one-tourist-out deletion. The deficit is extreme relative to the sampled null, while its class-level interpretation is undetermined and unstable. We give a four-step pre-interpretation check and a reference implementation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22014",
  "author_total": 1,
  "authors": [
    {
      "name": "Tengfei Shao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/438z2w1deh5b4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22014",
  "fulltext_url": null,
  "id": "438z2w1deh5b4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22014",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SI"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7213876395",
  "pdf_url": "https://arxiv.org/pdf/2609.22014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/438z2w1deh5b4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:12Z",
      "native_id": "2609.22014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Auditing bipartite motif interpretations: a worked example with conservation checks and open-path decomposition",
  "title_text": "Auditing bipartite motif interpretations: a worked example with conservation checks and open-path decomposition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:12Z",
  "url": "https://research.draconitic.com/paper/438z2w1deh5b4",
  "venue": "arXiv",
  "versions": []
}