Modeling Intertwined Humanity: Neutrosophic Complete Graphs, Ubuntu, and the Logic of No

Abstract

The human experience, at its most fundamental level, is one of interconnectedness. No 
individual exists in isolation; identities are forged, values are shaped, and realities are 
co-constructed within a complex web of relationships. Yet, traditional Western philosophical and 
scientific models often emphasize individualism and discrete entities, probably influenced by 
traditional Aristotelian logic, struggling to fully capture the fluid, ambiguous, and often 
contradictory nature of these interdependencies. The challenge, then, is to develop a modeling 
framework capable of expressing such profound and multi-faceted entanglement, especially when 
relationships are characterized by ambiguity, partial truths, or even co-existing contradictions. 
Classical graph theory, with its binary edges (either a connection exists or it does not), falls short. 
This article argues that the Neutrosophic complete graph, a powerful extension of fuzzy and 
intuitionistic fuzzy graph theory, offers a promising mathematical instrument for precisely this 
purpose. By incorporating degrees of truth, falsehood, and crucially, indeterminacy (or 
neutrality/hesitancy) into its representation of nodes and relationships, the Neutrosophic complete 
graph can provide a sophisticated and nuanced model for the intertwined humanity perceived in 
Ubuntu and the complex non-dualistic insights of the "logic of not," thereby mirroring the 
irreducible dependency found in Borromean rings.

DOI: 10.5281/zenodo.15758982