In this paper, we present CensNet, Convolution with Edge-Node Switching graph neural network, for semi-supervised classification and regression in graph-structured data with both node and edge features. CensNet is a general graph embedding framework, which embeds both nodes and edges to a latent feature space. By using line graph of the original undirected graph, the role of nodes and edges are switched, and two novel graph convolution operations are proposed for feature propagation. Experimental results on real-world academic citation networks and quantum chemistry graphs show that our approach has achieved or matched the state-of-the-art performance.