Metrics for Multiset-Theoretic Subgraphs

Abstract

We show how to define a plethora of metrics for graphs—either full graphs or subgraphs. The method mainly utilizes the minimal matching between any two multisets of positive real numbers by comparing the multiple edges with respect to their corresponding vertices. In the end of this article, we also demonstrate how to implement these defined metrics with the help of adjacency matrices. These metrics are easy to be manipulated in real applications and could be amended according to different situations. By our metrics, one should be able to compare the distances between graphs, trees, and networks, in particular those with fuzzy properties.