Modelling the dynamics of urban venues is a challenging task as it is multifaceted in nature. Demand is a function of many complex and nonlinear features such as neighborhood composition, real-time events, and seasonality. Recent advances in Graph Convolutional Networks (GCNs) have had promising results as they build a graphical representation of a system and harness the potential of deep learning architectures. However, there has been limited work using GCNs in a temporal setting to model dynamic dependencies of the network. Further, within the context of urban environments, there has been no prior work using dynamic GCNs to support venue demand analysis and prediction. In this paper, we propose a novel deep learning framework which aims to better model the popularity and growth of urban venues. Using a longitudinal dataset from location technology platform Foursquare, we model individual venues and venue types across London and Paris. First, representing cities as connected networks of venues, we quantify their structure and note a strong community structure in these retail networks, an observation that highlights the interplay of cooperative and competitive forces that emerge in local ecosystems of retail businesses. Next, we present our deep learning architecture which integrates both spatial and topological features into a temporal model which predicts the demand of a venue at the subsequent time-step. Our experiments demonstrate that our model can learn spatio-temporal trends of venue demand and consistently outperform baseline models. Relative to state-of-the-art deep learning models, our model reduces the RSME by ~ 28% in London and ~ 13% in Paris. Our approach highlights the power of complex network measures and GCNs in building prediction models for urban environments. The model could have numerous applications within the retail sector to better model venue demand and growth.