Problem

The concept of decentralization in computer science has lacked a universally accepted, transferable definition for over fifty years, leading to significant inconsistencies in system analysis across diverse domains like AI, distributed computing, and IoT. Current approaches often conflate decentralization with related notions such as distribution or trust, or define it through specific technologies like blockchain, making comparisons and formal reasoning difficult. This paper identifies four key problems: definitional ambiguity due to context-dependent interpretations, persistent confusion between decentralization (relational structure) and distribution (component placement), a lack of structural formalism concentrating on node-centric metrics rather than inherent relational properties, and the absence of transferable quantification methods that work across different system architectures.

Method

To address the Decentralization Problem, this work introduces a novel graph-based ontology, structured into four interconnected layers. The Ontological Layer establishes graph-theoretic realism, viewing systems as configurations of entities and interconnections, evaluated at fixed temporal points, and adopting a multi-dimensional approach to subjects of decentralization. The Logical Layer formalizes these concepts with explicit semantics, axioms, and proofs of consistency, satisfiability, and entailment, defining terms like "Centralized Subject" (multiplicity of one) and "Decentralized Subject" (multiplicity greater than one). The Modeling Layer bridges the abstract ontology to computational representation by mapping subject realizations to vertices, distinguishing between the number of distinct realizations (multiplicity, δ) and the number of distinct supporting vertices (distribution, λ). Finally, the Analytical Layer introduces two subject-specific, graph-based metrics: Void Tolerance, which quantifies a system's resilience to vertex removal, and Imperviousness, which measures the effort required to compromise connectivity via edge removal. These metrics combine into a two-dimensional vector per subject, enabling multi-dimensional evaluation and aggregation of decentralization across a system. A browser-based application prototype implements this framework for interactive modeling and analysis.

Results

The proposed ontological framework was validated through case studies on federated learning and blockchain architectures, demonstrating its ability to provide consistent classifications and detailed analytical insights where existing methods fall short. In federated learning, a vanilla star-topology system was classified as "Partially Decentralized" because data storage and model training were decentralized, but aggregation authority remained centralized. Conversely, a decentralized federated learning setup with collaborative aggregation was deemed "Fully Decentralized" as all subjects exhibited decentralization. Similarly, two blockchain instantiations with identical topologies but differing functional assignments yielded distinct decentralization profiles, with one being "Partially Decentralized" (centralized consensus) and the other "Fully Decentralized" (decentralized consensus and ledger replication). The analytical metrics, Void Tolerance and Imperviousness, successfully exposed specific structural and functional vulnerabilities for each subject within these systems, providing a richer characterization than traditional scalar measures. For instance, transaction submission in one blockchain example showed high Void Tolerance but low Imperviousness, indicating robustness against node removal but fragility against edge removal. The comparative analysis using aggregated subject vectors allowed for quantitative claims that one system was "more" decentralized than another, clearly identifying the contributing factors.

Implications

This work provides a crucial formal separation between decentralization and distribution, defining the former by realization multiplicity and the latter by topological placement, which clarifies long-standing conceptual ambiguities. By emphasizing the relational structure of systems through a graph-based ontology, it moves beyond the limitations of node-centric analyses that overlook critical connectivity information. The multi-dimensional decentralization vector, derived from Void Tolerance and Imperviousness, offers a substantially richer and more granular characterization than existing scalar metrics, enabling detailed reasoning about system robustness and vulnerabilities on a subject-by-subject basis. This vector representation also facilitates direct visualization and cross-contextual comparison of decentralization profiles, allowing practitioners to identify shared architectural weaknesses across different application domains. The ontological approach effectively bridges informal intuitions about decentralization with formal reasoning, offering a robust and transferable foundation for analyzing computer communication systems. While the framework intentionally focuses on structural properties and static snapshots, and the specific functional forms of the metrics are purpose-built, it provides a transparent and rigorous methodology that reduces conceptual circularity and lays the groundwork for future advancements in understanding and designing truly decentralized systems.