Maximum Common Subelement Metrics and its Applications to Graphs

TL;DR

This paper introduces the Maximum Common Subelement (MCS) Model, generalizes graph metrics, and explores their applications, including modeling complex labeled graphs and relating to graph edit distance.

Contribution

It characterizes the MCS Model, proves four metrics on it, and extends graph metrics to complex labeled graphs, connecting to graph edit distance.

Findings

Four metrics on MCS Model are proven to exist.

Generalization of graph metrics to complex labels.

Relation established between graph edit distance and MCS.

Abstract

In this paper we characterize a mathematical model called Maximum Common Subelement (MCS) Model and prove the existence of four different metrics on such model. We generalize metrics on graphs previously proposed in the literature and identify new ones by showing three different examples of MCS Models on graphs based on (1) subgraphs, (2) induced subgraphs and (3) an extended notion of subgraphs. This latter example can be used to model graphs with complex labels (e.g., graphs whose labels are other graphs), and hence to derive metrics on them. Furthermore, we also use (3) to show that graph edit distance, when a metric, is related to a maximum common subelement in a corresponding MCS Model.