A Note on the Modeling Power of Different Graph Types

TL;DR

This paper introduces a partial order to compare the expressivity of different graph types and shows that all attributed graphs share the same modeling power, clarifying their relative capabilities.

Contribution

It establishes a formal framework to compare graph types based on their expressivity and demonstrates the equal modeling power of attributed graphs.

Findings

All attributed graph types are equally expressive.

A partial order on graph types based on expressivity is proposed.

The framework clarifies the relative modeling power of various graph types.

Abstract

Graphs can have different properties that lead to several graph types and may allow for a varying representation of diverse information. In order to clarify the modeling power of graphs, we introduce a partial order on the most common graph types based on an expressivity relation. The expressivity relation quantifies how many properties a graph type can encode compared to another type. Additionally, we show that all attributed graph types are equally expressive and have the same modeling power.