We propose a graph-based tracking formulation for multi-object tracking (MOT) where target detections contain kinematic information and re-identification features (attributes). Our method applies a successive shortest paths (SSP) algorithm to a tracking graph defined over a batch of frames. The edge costs in this tracking graph are computed via message-passing network, a graph neural network (GNN) variant. The parameters of the GNN, and hence, the tracker, are learned end-to-end on a training set of example ground-truth tracks and detections. Specifically, learning takes the form of bilevel optimization guided by our novel loss function. We evaluate our algorithm on simulated scenarios to understand its sensitivity to scenario aspects and model hyperparameters. Across varied scenario complexities, our method compares favorably to a strong baseline.