Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications

Many real-world systems involve uncertainty not only in individual attributes but also in the relationships between entities. To address this, a variety of graph-theoretic frameworks have been developed that incorporate uncertainty directly into vertices, edges, and higher-level structural properties. Among these, fuzzy graphs, intuitionistic fuzzy graphs, neutrosophic graphs, and plithogenic graphs represent key approaches to modeling uncertainty in network structures. This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision-making systems, graph neural networks, knowledge graphs, and cognitive maps. By organizing diverse uncertainty-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems.