论文标题
测量定向超图上的动态系统
Measuring dynamical systems on directed hyper-graphs
论文作者
论文摘要
网络和图形为大量系统提供了一个简单但有效的模型，这些模型在整个成对交互过程中相互作用。不幸的是，这样的模型无法描述所有构建块的系统以更高的阶段相互作用。高阶图为我们提供了适合任务的正确工具，但由于交互作用顺序引起了更高的计算复杂性。在本文中，我们分析了定向超图和线性动力学系统的结构之间的相互作用，即在其上定义的随机步行。一个人如何将网络度量（例如中心性或模块化）扩展到此框架？我们将测量与之相关的动力学系统，而不是通过HyperGraph框架重新定义网络测量，而是随之而来的复杂性提升。这种方法让我们对成对结构（例如过渡矩阵）采取已知措施，并确定可容纳这种程序的措施家族。
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact at a higher order. Higher order graphs provide us the right tools for the task, but introduce a higher computing complexity due to the interaction order. In this paper we analyze the interplay between the structure of a directed hypergraph and a linear dynamical system, a random walk, defined on it. How can one extend network measures, such as centrality or modularity, to this framework? Instead of redefining network measures through the hypergraph framework, with the consequent complexity boost, we will measure the dynamical system associated to it. This approach let us apply known measures to pairwise structures, such as the transition matrix, and determine a family of measures that are amenable of such procedure.
