Problems in distributed security often naturally map to graphs. The centrality of nodes assesses the importance of nodes in a graph. It is used in various applications. Cooperative game theory has been used to create nuanced and flexible notions of node centrality. However, the approach is often computationally complex to implement classically. This work describes a quantum approach to approximating the importance of nodes that maintain a target connection. In addition, we detail a method for quickly identifying high-importance nodes. The approximation method relies on quantum subroutines for st-connectivity and approximating Shapley values. The search for important nodes relies on a quantum algorithm to find the maximum. We consider st-connectivity attack scenarios in which a. malicious actor disrupts a subset of nodes to perturb the system functionality. Our methods identify the nodes that are most important in minimizing the impact of the attack. The node centrality metric identifies where more redundancy is required and can be used to enhance network resiliency. Finally, we explore the potential complexity benefits of our quantum approach in contrast to classical random sampling.