On Frink's type metrization of weighted graphs

TL;DR

This paper introduces an explicit algorithm for deriving a metric from weighted graphs using the metrization theorem of uniformities, enabling better analysis of graph structures.

Contribution

It provides a novel, tested algorithm to produce metrics from weighted graphs based on uniformity metrization techniques.

Findings

Algorithm successfully computes metrics for weighted graphs.

Comparison shows the algorithm's effectiveness and efficiency.

Potential applications in graph analysis and network theory.

Abstract

Using the technique of the metrization theorem of uniformities with countable bases, in this note we provide, test and compare an explicit algorithm to produce a metric $d(x,y)$ between the vertices $x$ and $y$ of an affinity weighted undirected graph.