Fuzzy Centrality Measures: A Survey

Most real-world problems can be pictured as a set of connections and interactions between various entities. Together, these entities create a complex phenomenon investigated in the form of complex networks. Each of the entities in the network plays a particular role in the definition of the structure and the analysis of the studied problem. Several measures of centrality have been proposed in the literature to estimate the contribution and quantify the relevance of network entities. The most influential nodes are defined either locally, via the measurement of their connections with their directly related neighbors, or globally, via the measurement of the importance of their neighbors or their relevance in terms of contribution to the fast propagation of information based on the shortest paths. Due to the incompleteness of real-world data, crisp representations do not adequately describe the problem. Therefore, fuzzy graphs have been proposed to give more realistic representations by taking into account the uncertainties present in data. This paper proposes a state of the art of fuzzy centrality measures with a focus on proposed studies on urban traffic networks. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.