We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

中文翻译：

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通过高阶超图走动进行超网络科学

我们提出高阶超图行走作为将基于图的网络科学技术推广到超图的框架。超图中的边入射是定量的，产生具有长度和宽度的超图走动。然后概括为超图的图方法包括连接的分量分析，基于图距离的度量（如紧密度中心）和基于基元的度量（如聚类系数）。我们将这些方法的高阶类似物应用于现实世界的超网络，并显示它们揭示了细微且可解释的结构，这些结构无法被基于图的方法检测到。最后，我们将三个生成模型应用于数据，发现基本超图属性（例如密度和度分布）不一定控制这些新的结构度量。