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 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.

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相互作用。许多多联体相互作用是不对称的，节点起着独特的作用。例如，在一个学术合作网络中，论文作者的顺序通常反映出他们对已完成工作的贡献的性质。为了对这些网络建模，我们引入了带注释的超图作为有向图的自然多态概括。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。为了便于使用带注释的超图进行数据分析，我们为这些结构构造了一个角色感知的配置空模型，并证明了从中进行采样的有效马尔可夫链蒙特卡洛方案。我们着手制定几种度量和算法来分析带注释的超图。其中的一些，例如分类性和模块性，自然可以概括二进式对等物。其他度量标准（例如局部角色密度）对于带注释的超图设置是唯一的。我们在六个数字社交网络上说明了我们的技术，并提供了有关Enron电子邮件数据集的详细案例研究。