System Engineering Concepts Modeled via SuperHyperGraphs: Entity–Relationship, Service Dependency, Change Impact, and Workflow Structures

Abstract

Graph theory provides a foundational framework for modeling pairwise relationships through vertices and edges [1, 2]. Hypergraphs extend this paradigm by allowing edges to connect any subset of vertices, capturing higher-order interactions [3], and SuperHyperGraphs introduce hierarchical structure via iterated powerset constructions [4, 5]. In systems engineering, specialized graph models—Entity–Relationship Graphs for database schema design, Service Dependency Graphs for incident impact analysis, Change Impact Graphs for assessing configuration-change risks, and ITIL Workflow Graphs for process automation—are widely used. In this paper, we show how each of these models can be formulated and enriched as hypergraphs and ?-layer SuperHyperGraphs, thereby enabling multi-way relationships and multi-scale hierarchical analysis.