The degree of connectivity among hospital wards and the dynamic nonlinear flow of patients cause bottlenecks to begin in non-priority wards, accumulate within the paths, distribute throughout the hospital, and emerge as overflow in crucial wards. This requires a network-based modeling approach to address the bottlenecks caused by second- and third-order wards and to significantly influence the overall and emergent performance of multiple wards. Understanding the relative merits of different network modeling and analysis approaches in this complex environment is often challenging and requires a holistic strategy to identify persistent bottlenecks and provide evidence-based scenarios. This article introduces a novel hybrid modeling approach that integrates network analysis algorithms and agent-based network simulation of patient flow over a complete hospital network. Through network analysis, such as structural hole and flow algorithms, the approach identifies common persistent bottlenecks from the flow and structural perspectives, while percolation and perturbation analyses measure the performance improvement of wards based on variations in patient flow, and the simulations enable the investigation of scenarios. The results indicate the wards and patient types that can contribute to improving the hospital’s performance. The proposed approach facilitates holistic, dynamic modeling of hospitals, irrespective of their network scale, and enables the identification of bottleneck sources and their associated paths, contributing to a comprehensive assessment of the system’s performance.