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September 5, 2025Open Access

Some Meta-Graph Structures: Mixed Graph, DiHyperGraph, Knowledge Graph, Intersection Graph, and Chemical Graph

Key Points

Metagraphs enable a hierarchy of graph structures, improving understanding of relationships among different graph types.
This exploration involves mixed graphs, dihypergraphs, and knowledge graphs, highlighting their interconnections and potential applications.
Analyzing these graphs within the metagraph framework uses vertices as graphs, forming a recursive structure that enhances existing models.
The findings suggest expanded applications in various fields, necessitating further research on metagraph structures and their utility.

Abstract

Graph theory studies mathematical structures composed of vertices and edges in order to model relationships and connectivity 1, 2. A MetaGraph is a higher-level construct in which the vertices are themselves graphs, and the edges represent specified relations among those graphs. An Iterated MetaGraph extends this concept recursively: its vertices are MetaGraphs, producing a hierarchy of graph-of-graphs structures across multiple levels. In this work, we explore the possibility of extending Mixed Graphs, DiHyperGraphs, Knowledge Graphs, Intersection Graphs, and Chemical Graphs within the framework of MetaGraphs and Iterated MetaGraphs.

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Takao Fujita (Wed,) studied this question.

synapsesocial.com/papers/68bb3a2b2b87ece8dc954993 https://doi.org/https://doi.org/10.26434/chemrxiv-2025-9pxz7