A metric on the space of weighted graphs

TL;DR

This paper introduces a new metric for weighted graphs that measures their similarity, proves the space's completeness, and explores its analytical properties, with potential applications in pattern and face recognition.

Contribution

It presents a novel metric for weighted graphs and demonstrates the completeness of the resulting metric space, expanding analytical tools for graph comparison.

Findings

The metric effectively measures distances between weighted graphs.

The space of weighted graphs with this metric is complete.

Analytical properties of the space are characterized.

Abstract

In this paper we offer a metric similar to graph edit distance which measures the distance between two (possibly infinite)weighted graphs with finite norm (we define the norm of a graph as the sum of absolute values of its edges). The main result is the completeness of the space. Some other analytical properties of this space are also investigated. The introduced metric could have some applications in pattern recognition and face recognition methods.