Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian regularization framework, GCNs perform an implicit Laplacian type regularization to capture local graph structure. In this work, we propose Lovász Convolutional Network (LCNs) which are capable of incorporating global graph properties. LCNs achieve this by utilizing Lovász's orthonormal embeddings of the nodes. We analyse local and global properties of graphs and demonstrate settings where LCNs tend to work better than GCNs. We validate the proposed method on standard random graph models such as stochastic block models (SBM) and certain community structure based graphs where LCNs outperform GCNs and learn more intuitive embeddings. We also perform extensive binary and multi-class classification experiments on real world datasets to demonstrate LCN's effectiveness. In addition to simple graphs, we also demonstrate the use of LCNs on hyper-graphs by identifying settings where they are expected to work better than GCNs. © Copyright 2019 by the author(s).