Hospitals are complex systems and optimising their function is critical to the provision of high quality, cost effective healthcare. Nevertheless, metrics of performance have to date focused on the performance of individual elements rather than the system as a whole. Manipulation of individual elements of a complex system without an integrative understanding of its function is undesirable and may lead to counter-intuitive outcomes and a holistic metric of hospital function might help design more efficient services. We aimed to characterise the system of peri-operative care for emergency surgical admissions in our tertiary care hospital using network analysis. We used retrospective electronic health record data to construct a weighted directional network of the system. For this we selected all unplanned admissions during a 3.5 year period involving a surgical intervention during the inpatient stay and obtained a set of 16,500 individual inpatient episodes. We then constructed and analysed the structure of this network using established methods from network science such as degree distribution, betweenness centrality and small-world characteristics. The analysis showed the service to be a complex system with scale-free, small-world network properties. This finding has implications for the structure and resilience of the service as such networks, whilst being robust in general, may be vulnerable to outages at specific key nodes. We also identified such potential hubs and bottlenecks in the system based on a variety of network measures. It is hoped that such a holistic, system-wide description of a hospital service may provide better metrics for hospital strain and serve to help planners engineer systems that are as robust as possible to external shocks.