What is actually a metric graph? (1912.07549v2)

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.