The importance of collaboration and teamwork has been widely acknowledged in various scientific fields. Although network analysis has been applied in many scientific domains to study the structure of collaboration networks, to the best of our knowledge, no study has thus far considered perioperative teams at the enterprise scale. Due to the specific characteristics of the surgical service providers network (e.g., being highly patient-centered), we hypothesize it has a scale-free topology. Scale-free networks exhibit important characteristics such as the existence of “hub” nodes that have a much higher degree than other nodes, and play a crucial role in the network. In this paper, we examined the intra- and postoperative networks of surgeons, anaesthesiologists, nurses, postoperative consultants, and other surgical service providers to verify the existence of the scale-free property and to analyze its trend over time. Our results confirm the existence of scale-free topology in the intraoperative network, and partially for the postoperative network. Additionally, we observed a declining trend of the scale-free property in the postoperative segment over time.