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Reconstructing Portal Vein and Hepatic Vein trees from contrast enhanced abdominal CT scans is a prerequisite for preoperative liver surgery simulation. Existing deep learning based methods treat vascular tree reconstruction as a semantic segmentation problem. However, vessels such as hepatic and portal vein look very similar locally and need to be traced to their source for robust label assignment. Therefore, semantic segmentation by looking at local 3D patch results in noisy misclassifications. To tackle this, we propose a novel multi-task deep learning architecture for vessel tree reconstruction. The network architecture simultaneously solves the task of detecting voxels on vascular centerlines (i.e. nodes) and estimates connectivity between center-voxels (edges) in the tree structure to be reconstructed. Further, we propose a novel connectivity metric which considers both inter-class distance and intra-class topological distance between center-voxel pairs. Vascular trees are reconstructed starting from the vessel source using the learned connectivity metric using the shortest path tree algorithm. A thorough evaluation on public IRCAD dataset shows that the proposed method considerably outperforms existing semantic segmentation based methods. To the best of our knowledge, this is the first deep learning based approach which learns multi-label tree structure connectivity from images.