Reinforced by the COVID-19 pandemic, the capacity of health systems to cope with increasing healthcare demands has been an abiding concern of both governments and the public. Health systems are made up from non-identical human and physical components interacting in diverse ways in varying locations. It is challenging to represent the function and dysfunction of such systems in a scientific manner. We describe a Network Science approach to that dilemma. General hospitals with large emergency caseloads are the resource intensive components of health systems. We propose that the care-delivery services in such entities are modular, and that their structure and function can be usefully analysed by contemporary Network Science. We explore that possibility in a study of Australian hospitals during 2019 and 2020. We accessed monthly snapshots of whole of hospital administrative patient level data in two general hospitals during 2019 and 2020. We represented the organisations inpatient services as network graphs and explored their graph structural characteristics using the Louvain algorithm and other methods. We related graph topological features to aspects of observable function and dysfunction in the delivery of care. We constructed a series of whole of institution bipartite hospital graphs with clinical unit and labelled wards as nodes, and patients treated by units in particular wards as edges. Examples of the graphs are provided. Algorithmic identification of community structures confirmed the modular structure of the graphs. Their functional implications were readily identified by domain experts. Topological graph features could be related to functional and dysfunctional issues such as COVID-19 related service changes and levels of hospital congestion. Contemporary Network Science is one of the fastest growing areas of current scientific and technical advance. Network Science confirms the modular nature of healthcare service structures. It holds considerable promise for understanding function and dysfunction in healthcare systems, and for reconceptualising issues such as hospital capacity in new and interesting ways.