On Edge-MetaGraph
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This paper studies graph-based higher-order structures related to metagraphs and edgelabeled 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 EdgeMetaGraphs 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.