Short-term demand prediction is important for managing transportation infrastructure, particularly in times of disruption, or around new developments. Many bike-sharing schemes face the challenges of managing service provision and bike fleet rebalancing due to the “tidal flows” of travel and use. For them, it is crucial to have precise predictions of travel demand at a fine spatiotemporal granularities. Despite recent advances in machine learning approaches (e.g. deep neural networks) and in short-term traffic demand predictions, relatively few studies have examined this issue using a feature engineering approach to inform model selection. This research extracts novel time-lagged variables describing graph structures and flow interactions from real-world bike usage datasets, including graph node Out-strength, In-strength, Out-degree, In-degree and PageRank. These are used as inputs to different machine learning algorithms to predict short-term bike demand. The results of the experiments indicate the graph-based attributes to be more important in demand prediction than more commonly used meteorological information. The results from the different machine learning approaches (XGBoost, MLP, LSTM) improve when time-lagged graph information is included. Deep neural networks were found to be better able to handle the sequences of the time-lagged graph variables than other approaches, resulting in more accurate forecasting. Thus incorporating graph-based features can improve understanding and modelling of demand patterns in urban areas, supporting bike-sharing schemes and promoting sustainable transport. The proposed approach can be extended into many existing models using spatial data and can be readily transferred to other applications for predicting dynamics in mass transit systems. A number of limitations and areas of further work are discussed.