Reversible matrices, labelled graphs, and labelled 2 structures

[Laurent Lyaudet]

Hello,

I am from a background in graph theory and I discovered graph databases recently.

I wrote a research article with my functional point of view instead of the classical relational point of view in graph theory logic.

I tried to make the introduction of my article as friendly and easy to grasp the core concepts as possible.

I wanted to share my article with you :

https://web.archive.org/web/20201230092310/http://lyaudet.eu/laurent/Publi/Journaux/LL2020LargeursStructuresBinaires/LL2020LargeursStructuresBinaires_v5.pdf

In the introduction I show that GraphQL queries can be solved on a reversible matrix instead of a multigraph. There is one trivial theorem where you just transform edges/arcs into new vertices using the incidency graph.

And there is a slightly less trivial theorem where you transform multi-edges with properties between vertices into a single integer value from one vertex to another.

The slightly less trivial theorem can, nevertheless, only be done for a fragment of GraphQL.

I don't know if any of these theorems can be made efficient and have practical applications but maybe some of you will enjoy to have a logical framework that fits graph databases.

May I ask for your feedback, please ?

Best regards,

    Laurent Lyaudet