Centrality measures play a crucial role in identifying the most important nodes in a network, with applications ranging from social networks to biological systems. Traditional centrality on classical graph theory, which may struggle to capture complex interactions in large and interconnected systems. Quantum graphs, integrating quantum principles such as superposition and entanglement, offer a novel framework for evaluating centrality. By representing nodes and edges with quantum states, quantum graphs can account for both direct and indirect relationships with greater precision. This study introduces quantum centrality measures, showing how entangled edges and dynamic vertex states can reveal more nuanced insights into node importance. We apply these quantum centrality measures to various real-world networks, such as social, transportation, and communication networks.