论文标题
定向超图中的互惠：措施，发现和发电机
Reciprocity in Directed Hypergraphs: Measures, Findings, and Generators
论文作者
论文摘要
小组互动在各个领域都普遍。其中许多，包括电子邮件交换，化学反应和比特币交易，都是定向性的，因此它们自然地建模为定向超图，其中每个HyperArc由一组源节点和一组目标节点组成。对于有针对性超图的特殊情况的有向图，互惠在揭示图形的组织原理和求解图形学习任务方面起着关键作用。但是，对于一般的定向超图，即使没有制定系统的互惠量度。在这项工作中，我们研究了11种实际超图的互惠。为此，我们首先介绍了八个公理，任何合理的互惠措施都应满足。其次，我们提出了HyperRec，这是一个满足所有公理的原则性测量量度。第三，我们开发了一种用于计算该度量的快速且精确的算法，其搜索空间高达10^{147} x X x小于幼稚计算。第四，使用它们，我们检查了11个现实世界中的超图，并发现将它们与随机超图形区分开的模式。最后，我们提出了Redi，这是一种直观的生成模型，用于表现出模式的定向超图。
Group interactions are prevalent in a variety of areas. Many of them, including email exchanges, chemical reactions, and bitcoin transactions, are directional, and thus they are naturally modeled as directed hypergraphs, where each hyperarc consists of the set of source nodes and the set of destination nodes. For directed graphs, which are a special case of directed hypergraphs, reciprocity has played a key role as a fundamental graph statistic in revealing organizing principles of graphs and in solving graph learning tasks. For general directed hypergraphs, however, even no systematic measure of reciprocity has been developed. In this work, we investigate the reciprocity of 11 real-world hypergraphs. To this end, we first introduce eight axioms that any reasonable measure of reciprocity should satisfy. Second, we propose HyperRec, a family of principled measures of hypergraph reciprocity that satisfies all the axioms. Third, we develop Ferret, a fast and exact algorithm for computing the measure, whose search space is up to 10^{147}x smaller than that of naive computation. Fourth, using them, we examine 11 real-world hypergraphs and discover patterns that distinguish them from random hypergraphs. Lastly, we propose ReDi, an intuitive generative model for directed hypergraphs exhibiting the patterns.
