基于高阶超图游动的超网络科学
Hypernetwork Science via High-Order Hypergraph Walks
摘要：
我们提出高阶超图游走作为一个框架，推广基于图的网络科学技术超图。超图中的边关联是定量的，从而产生具有长度和宽度的超图游动。然后推广到超图的图方法包括连通分量分析，基于图距离的度量（如接近中心性）和基于图案的度量（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，并表明它们揭示了基于图的方法无法检测到的细微差别和可解释的结构。最后，我们将三种生成模型应用于数据，并发现基本的超图属性，如密度和度分布，并不一定控制这些新的结构测量。我们的工作演示了如何分析超图结构的数据更丰富的时候，利用工具量身定制，以捕捉超图原生现象，并建议一个可能的途径实现这一目标。
英文摘要：
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.
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