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arXiv · 2208.07246

A measure-theoretic representation of graphs

Raffaella Mulas·Giulio Zucal
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Abstract

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.

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Raffaella Mulas, Giulio Zucal. 2023-01-04. A measure-theoretic representation of graphs. https://arxiv.org/abs/2208.07246

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