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Traffic prediction is an important and yet highly challenging problem due to the complexity and constantly changing nature of traffic systems. To address the challenges, we propose a graph and attentive multi-path convolutional network (GAMCN) model to predict traffic conditions such as traffic speed across a given road network into the future. Our model focuses on the spatial and temporal factors that impact traffic conditions. To model the spatial factors, we propose a variant of the graph convolutional network (GCN) named LPGCN to embed road network graph vertices into a latent space, where vertices with correlated traffic conditions are close to each other. To model the temporal factors, we use a multi-path convolutional neural network (CNN) to learn the joint impact of different combinations of past traffic conditions on the future traffic conditions. Such a joint impact is further modulated by an attention} generated from an embedding of the prediction time, which encodes the periodic patterns of traffic conditions. We evaluate our model on real-world road networks and traffic data. The experimental results show that our model outperforms state-of-art traffic prediction models by up to 18.9% in terms of prediction errors and 23.4% in terms of prediction efficiency.