Graph characteristics are often studied through various parameters, with ongoing research dedicated to exploring these aspects. Among these, graph width parameters—such as tree-width—are particularly important due to their practical applications in algorithms and real-world problems. A hypergraph generalizes traditional graph theory by abstracting and extending its concepts [77]. More recently, the concept of a SuperHyperGraph has been introduced as a further generalization of the hypergraph. Neutrosophic logic [133], a mathematical framework, extends classical and fuzzy logic by allowing the simultaneous consideration of truth, indeterminacy, and falsity within an interval. In this paper, we explore Superhypertree-width, Neutrosophic tree-width, and t-Neutrosophic tree-width.