Architectural descriptions of complex systems are commonly centered around diagrams, viewpoints, and notational frameworks. This paper proposes a minimal and complete architectural model in which any architecture is fully determined by a set of objects and a set of directed relations between them. Architectural analysis is formulated in terms of canonical graph operators, and all diagrams, views, and viewpoints are shown to be computable projections of a single underlying object–relation graph. By separating architectural ontology from representational artifacts, the model eliminates diagram-level redundancy and ensures invariance of architectural reasoning under changes of notation, tooling, or visualization. Structural properties such as reachability, path existence, and architectural vulnerability are derived directly from the graph topology rather than from operational metrics. Inspired by the principles of the Architecture of Complex Systems (ACS), the paper provides a formal and tool-independent foundation for architectural analysis, comparison, and evolution. A reference implementation at the relational database level demonstrates the practical viability of the proposed approach without coupling architectural reasoning to visualization artifacts.
Alexey A. Nekludoff (Wed,) studied this question.
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