aspg-33-4472-1792223312 20261017074832 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2026 13 2 Takaaki Fujita Independent Researcher, Tokyo, Japan Ajoy Kanti Das Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India Suman Das Assistant Professor Grade II (Mathematics), Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, India Sankar Prasad Mondal Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, West Bengal, India Volkan Duran Department of Computer Engineering, Igdır University, Turkey This paper studies graph-based higher-order structures related to metagraphs and edge-labeled hierarchical networks. After reviewing MetaGraphs and Iterated MetaGraphs, we introduce the notion of an Edge-MetaGraph, in which each edge is labeled by a two-ported internal graph, allowing edge-substitution expansion through port gluing. We then define Iterated Edge-MetaGraphs recursively, so that edges may carry nested Edge-MetaGraph structures. Concrete examples from biomedical systems, software pipelines, and logistics are presented to illustrate the expressive power of the proposed framework 2026 10 16 4472 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.130203 https://americaspg.com/journal/33/article/4472 https://americaspg.com/storage/articles/manuscripts/01KYNCJ1SMP7J8NAXMMY6VZT01.pdf