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Line clouds, though under-investigated in the previous work, potentially encode more compact structural information of buildings than point clouds extracted from multi-view images. In this work, we propose the first network to process line clouds for building wireframe abstraction. The network takes a line cloud as input , i.e., a nonstructural and unordered set of 3D line segments extracted from multi-view images, and outputs a 3D wireframe of the underlying building, which consists of a sparse set of 3D junctions connected by line segments. We observe that a line patch, i.e., a group of neighboring line segments, encodes sufficient contour information to predict the existence and even the 3D position of a potential junction, as well as the likelihood of connectivity between two query junctions. We therefore introduce a two-layer Line-Patch Transformer to extract junctions and connectivities from sampled line patches to form a 3D building wireframe model. We also introduce a synthetic dataset of multi-view images with ground-truth 3D wireframe. We extensively justify that our reconstructed 3D wireframe models significantly improve upon multiple baseline building reconstruction methods. The code and data can be found at https://github.com/Luo1Cheng/LC2WF.