The aim of this thesis is to gain insights into the impact that various variables have on the topological evolution of a public transit network in a polycentric urban region. These variables are: the spatial structure of the polycentric urban region, the demand distribution, the operational costs and multimodality versus unimodality. To gain these insights, a network evolution model is developed that incorporates these four variables. This network evolution model is then also applied to the Randstad public transit network to gain insights into potential improvements that can be made in this network and also to test the applicability of the model to a public transit network in practice.