Identifying influential nodes in complex networks is a fundamental challenge for understanding how information, influence, and contagion propagate through interconnected systems. Conventional centrality measures, particularly gravity-based models, often depend on pairwise interaction forces and a fixed radius of influence, which oversimplify the heterogeneous and dynamic nature of real networks. To overcome these limitations, this study proposes a novel non-interactive, action-based model, termed Yukawa Potential Centrality (YPC), which adapts the physical Yukawa potential to the topology of complex networks. Unlike gravity models, YPC computes a scalar potential for each node rather than pairwise forces, dynamically adjusting its radius of influence according to local structural properties. This formulation establishes a physically interpretable bridge between potential theory and network science, while significantly reducing computational complexity, from quadratic to near-linear time. The model is evaluated across both synthetic and real-world social networks, and its node rankings are compared with classical centrality indices and epidemic spreading models (SI and SIS). Experimental findings reveal that YPC exhibits a strong positive correlation with the SIS model and effectively isolates key spreaders, even within highly irregular topologies. These results demonstrate that YPC provides a scalable, adaptive, and theoretically grounded framework for influence analysis in social, biological, and communication networks.