Fuzzy centrality measures in social network analysis: Theory and application in a university department collaboration network

The motivation behind this research stems from the inherent complexity and vagueness in human social interactions, which traditional Social Network Analysis (SNA) approaches often fail to capture adequately. Conventional SNA methods typically represent relationships as binary or weighted ties, thereby losing the subtle nuances and inherent uncertainty in real-world social connections. The need to preserve the vagueness of social relations and provide a more accurate representation of these relationships motivates the introduction of a fuzzy-based approach to SNA. This paper proposes a novel framework for Fuzzy Social Network Analysis (FSNA), which extends traditional SNA to accommodate the vagueness of relationships. The proposed method redefines the ties between nodes as fuzzy numbers rather than crisp values and introduces a comprehensive set of fuzzy centrality indices, including fuzzy degree centrality, fuzzy betweenness centrality, and fuzzy closeness centrality, among others. These indices are designed to measure the importance and influence of nodes within a network while preserving the uncertainty in the relationships between them. The applicability of the proposed framework is demonstrated through a case study involving a university department's collaboration network, where relationships between faculty members are analyzed using data collected via a fascinating mouse-tracking technique.