Meta- and hypergraph representations allow reducing the amount of processed data without losing the original information. This advantage determines the most promising area for their application: the problems of big data analysis, provided that this data can be described using a graph representation. The article proposes an approach to modeling hierarchical systems based on nested metagraphs. Category theory is used to eliminate ambiguity in the interpretation of concepts. Formalized descriptions of static and dynamic nested metagraphs, methods for defining them, as well as basic operations are given. The basis of concepts, nested metagraphs is a monoid, as an information object, which is characterized by an internal form, internal and external contents. Thus, a monoid is a generalization of a graph structure and is interpreted as a vertex of a generalized graph.

Keywords: nested metagraph, metagraph monoid, metagraph adjacency matrix, operations on nested metagraphs

"The concept of the nested metagraph as the model of a complex object with different levels of generalization is introduced. It is shown that the nested metagraphs reflect the general system concept for description of complex objects with synergistic effect. This approach enables moving from the set-theoretic description of complex objects to their algebraic-theoretic description, thus increasing the model adequacy to real-life objects. The application of the nested metagraphs, in particular to business-intelligence and semantic search is considered. "

Keywords: nested metagraphs, complex object, hyperedge as the essence, business analysis, a semantic network