Complex neutrosophic vague soft graphs

In this paper, we present and expand on the idea of complex neutrosophic vague soft graphs (CNVSGs), a sophisticated framework for simulating vagueness, uncertainty and indeterminacy in complex systems. We characterise a strong complex neutrosophic vague soft graph (SCNVSG) as one in which, under soft set parameters, both the edges and vertices have complex-valued memberships and high levels of neutrosophic vagueness. A revised metric that takes into consideration a cumulative strength and uncertainty of connections within the graph properties, we also present the complement of a complex neutrosophic vague soft graph and the complement of a strong complex neutrosophic vague soft graph. In uncertain networks, a complement operations provide information about inverse behaviors and dual linkage. We further explore the notion of isomorphism and provide criteria for structural equivalence under complex neutrosophic inaccurate mappings. To demonstrate how the proposed ideas can be used, examples are provided. The theoretical results in this paper provide the way for future studies of complex uncertain networks, particularly in areas such as information fusion, cognitive modelling and decision support systems.