发表机构
Waseda University（早稻田大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过实例审计二部图模体解释，证明扇计数由度序列决定，并发现开放路径不足在零模型下显著但类别归因不稳定，提出预解释检查方法。
AI 中文摘要
二部图代理-对象网络（如游客-景点访问和顾客-商品交易）的模体轮廓被解读为关于结构角色和网络间差异的证据，但往往没有询问两个度序列已经确定了什么。在简单二部图中，一种节点类型上的诱导k-扇计数是度组合之和，因此在保持两个度序列的零假设下其方差为零。我们将这一已知结果应用于一个重建的旅游评分网络（17名游客、80个景点、637条边），这是唯一的推断性实例，并作为来源受限的说明，应用于已发表的36个月度奢侈品顾客-商品网络的模体实例聚合。四类扇是度序列的精确函数：在旅游网络中，原始扇计数和规模为3的二扇比率（84.7%扇出）重述了这些序列。已发表的奢侈品计数至少需要89,502条顾客-商品边，而报告的交易为26,451条，因此其99.8%的扇入仅作为描述性值报告。针对硬二部配置零模型，四环计数与度一致（z约+1.0），开放路径不足（z约-5.8），缺少2,243个实例，占零均值的2.4%；该不足在每次留一游客重跑中均存在（z在-4.5至-8.1之间）。一个精确恒等式在点估计处将其分解为64.4%混合和35.6%四环，但该分解并非归因：观察到的混合项低于所有500个零样本，两个分量在零模型下几乎共线（r=0.968），且在留一游客删除下混合份额范围从36.6%到116.5%。该不足相对于采样零模型是极端的，而其类别级解释是不确定且不稳定的。我们给出了一个四步预解释检查和一个参考实现。
英文摘要
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.
Comments52 pages, 8 figures, 10 tables. Submitted to PeerJ Computer Science. Analysis code and cached null ensembles: https://doi.org/10.5281/zenodo.22308052 ; tourism rating matrix: https://doi.org/10.5281/zenodo.22299150
