Fuzzy Semi-Directed Graphs: A Novel Approach for Modeling Complex Networks

Complex networks, permeating various domains, exhibit nonlinear dynamics, uncertain relationships, and complex interactions. Traditional graph theory representations are insufficient for capturing these intricacies. To address this, we introduce fuzzy semi-directed graphs, integrating fuzzy logic into semi-directed graphs. This novel approach enables the modeling of uncertain relationships, directed and undirected interactions, and complex dynamics. We establish mathematical foundations, propose new terminologies, and develop a centrality measure, fuzzy incidence centrality. This framework provides a comprehensive tool for analyzing complex networks, unveiling insights into node centrality and community structure. Applications in railway networks, road networks and telecommunication networks demonstrate the potential of fuzzy semi-directed graphs in understanding and optimizing complex systems.