论文标题
图形的措施理论表示
A measure-theoretic representation of graphs
论文作者
论文摘要
受图形极限理论中的动作收敛概念的启发，我们引入了矩阵的测量理论表示，并使用它来定义矩阵空间上的伪金属的新概念。此外，我们表明，这种伪金属是图形的邻接或拉普拉斯矩阵子空间上的度量标准。因此，特别是，我们获得了图形同构类别的度量。此外，我们研究了图表的某些特性如何在此度量表示中转化，并展示了我们的分析如何有助于对图形的动作收敛的更简单理解。
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metric on the space of matrices. Moreover, we show that such pseudo-metric is a metric on the subspace of adjacency or Laplacian matrices for graphs. Hence, in particular, we obtain a metric for isomorphism classes of graphs. Additionally, we study how some properties of graphs translate in this measure representation, and we show how our analysis contributes to a simpler understanding of action convergence of graphops.
