Strong Hub Number of a Fuzzy Graph

Abstract

In the study of fuzzy graphs, which generalize classical graphs by allowing varying degrees of membership for nodes and arcs, the concept of centrality becomes crucial for understanding the structural importance of nodes. One such centrality measure is the hub number, the minimum number of nodes (hubs) required. Every other node in the fuzzy graph is strongly adjacent to at least one hub with a degree of membership exceeding a given threshold. This paper introduces the formal definition of the hub number in the context of fuzzy graphs, explores its properties, and provides methods for its computation. Applications of the hub number include network design, information dissemination, and fuzzy social network analysis. The study offers theoretical insights and practical algorithms, contributing to the broader understanding of centrality in uncertain and imprecise network structures.