Analysis of the Metagraph Data Model in Terms of Metagraph Operations and Category Theory

A metagraph data model is a type of complex graph model designed to describe complex subject areas. Category theory is a well-known and well-researched mathematical apparatus that studies the properties of relations between various mathematical objects that do not depend on the internal structure of objects. In this article, we make an attempt to analyze the metagraph data model in terms of category theory. Operations over the metagraph are introduced and the properties of operations are considered in detail. The category of metagraphs “MetGr” is proposed, which is a category in which the object class is the set of metagraphs. Morphisms in such a category are based on a union operation. The proposed operations over the metagraph and the category of metagraphs “MetGr” is a necessary basis for further development of a rewriting system on metagraphs.