Graphs have become a crucial way to represent large, complex and often temporal datasets across a wide range of scientific disciplines. However, when graphs are used as input to machine learning models, this rich temporal information is frequently disregarded during the learning process, resulting in suboptimal performance on certain temporal infernce tasks. To combat this, we introduce Temporal Neighbourhood Aggregation (TNA), a novel vertex representation model architecture designed to capture both topological and temporal information to directly predict future graph states. Our model exploits hierarchical recurrence at different depths within the graph to enable exploration of changes in temporal neighbourhoods, whilst requiring no additional features or labels to be present. The final vertex representations are created using variational sampling and are optimised to directly predict the next graph in the sequence. Our claims are reinforced by extensive experimental evaluation on both real and synthetic benchmark datasets, where our approach demonstrates superior performance compared to competing methods, out-performing them at predicting new temporal edges by as much as 23% on real-world datasets, whilst also requiring fewer overall model parameters.