This study develops an Integer Programming (IP) approach to analytically estimate vertiport capacity envelopes. The approach is used to determine the sensitivity of vertiport capacity to the number and layout of touchdown and liftoff pads, taxiways, gates, and parking pads (i.e. the vertiport topology). The study also assesses the sensitivity of vertiport capacity to operational parameters including taxi time, turnaround time, pre-staged aircraft, and approach/departure procedure independence, among others. Findings indicate the importance of balancing the number of touchdown and liftoff pads with the number of gates to achieve maximum aircraft throughput per vertiport footprint. Furthermore, simultaneous paired arrivals or departures provide significant throughput gains without the need for fully independent approach and departure procedures. The methodology and findings introduced in this paper support the development of concepts of operation to maximize throughput for a given vertiport footprint and demand scenario. While throughput has been extensively researched for fixed-wing operations, little research has been dedicated to the operation of infrastructure for Vertical Takeoff and Landing (VTOL) aircraft. The emergence of new VTOL aircraft to conduct a potentially large number of urban air mobility operations creates a need to better understand the operation and throughput capacity of vertiports, especially in space constrained inner-city locations. This paper reviews numerous existing heliport designs to derive four topology classes of vertiport layouts. The IP formulation of vertiport operations is readily adapted to represent the infrastructure and operations of these layouts.