注释超图：模型与应用
Annotated Hypergraphs: Models and Applications
摘要：
超图提供了一种自然的建模语言，用于研究实体集之间的多元交互。许多多元交互是不对称的，节点扮演不同的角色。例如，在学术合作网络中，论文作者的顺序往往反映了他们对已完成工作的贡献的性质。为了对这些网络进行建模，我们引入了\emph{annotated hypergraphs}作为有向图的自然多元推广。带注释的超图形成了一个高度通用的框架，用于将元数据合并到多元图模型中。为了方便带注释超图的数据分析，我们为这些结构构造了一个角色感知的配置空模型，并证明了一个有效的马尔可夫链蒙特卡罗方案，从它的采样。其中的一些，如可拓性和模块性，自然推广并元对应。其他指标，如局部角色密度，是唯一的设置带注释的超图。我们说明了我们的技术在六个数字社交网络，并提出了详细的案例研究的安然电子邮件数据集。
英文摘要：
Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example, the order of authors on a paper often reflects the nature of their contributions to the completed work. To model these networks, we introduce \emph{annotated hypergraphs} as natural polyadic generalizations of directed graphs. Annotated hypergraphs form a highly general framework for incorporating metadata into polyadic graph models. To facilitate data analysis with annotated hypergraphs, we construct a role-aware configuration null model for these structures and prove an efficient Markov Chain Monte Carlo scheme for sampling from it. We proceed to formulate several metrics and algorithms for the analysis of annotated hypergraphs. Several of these, such as assortativity and modularity, naturally generalize dyadic counterparts. Other metrics, such as local role densities, are unique to the setting of annotated hypergraphs. We illustrate our techniques on six digital social networks, and present a detailed case-study of the Enron email data set.
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