What is actually a metric graph?
Combinatorics
2021-03-17 v2 Functional Analysis
General Topology
Abstract
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an abstract, self-contained definition of metric graph. Being mostly topological, it doesn't require any knowledge from graph theory and already determines uniquely several concepts that are commonly and unnecessarily \textit{defined} in the literature. Nevertheless, many ideas mentioned here are folklore in the quantum graph community: we discuss them for later reference.
Keywords
Cite
@article{arxiv.1912.07549,
title = {What is actually a metric graph?},
author = {Delio Mugnolo},
journal= {arXiv preprint arXiv:1912.07549},
year = {2021}
}