Hyperbolae Are No Hyperbole：Modeling Communities That Are Not Cliques（英语：Hyperbolae Are No Hyperbole：Modeling Communities That Are Not Cliques）
Hyperbolae Are No Hyperbole: Modelling Communities That Are Not Cliques
摘要：
集团经常被用来建模社区：社区是一组节点，其中每对节点都有可能连接。但研究现实世界的社区表明，它们的结构比这更多。特别是，节点可以以这样的方式排序，即社区中的（几乎）所有边都位于双曲线之下。在本文中，我们提出了三个新的模型，捕捉这种现象的社区。我们的模型解释了不同的社区结构，但我们也证明了它们在表达能力上是相同的。我们的模型比传统的块模型或以前提出的双曲线模型更适合真实世界的数据，这两种模型都是我们模型的特例。我们的模型还允许对参数进行直观的解释，使我们能够有效地总结图中社区的形状。
英文摘要：
Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much better than traditional block models or previously-proposed hyperbolic models, both of which are a special case of our model. Our models also allow for intuitive interpretation of the parameters, enabling us to summarize the shapes of the communities in graphs effectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
