Weighted Line Graph Convolutional Networks

Line graphs have shown to be effective in improving feature learning in graph neural networks. Line graphs can encode topology information of their original graphs and provide a complementary representational perspective. In this work, we show that the encoded information in line graphs is biased. To overcome this issue, we propose a weighted line graph that corrects biases in line graphs by assigning normalized weights to edges. Based on our weighted line graphs, we develop a weighted line graph convolution layer that takes advantage of line graph structures for better feature learning. In particular, it performs message passing operations on both the original graph and its corresponding weighted line graph. To address efficiency issues in line graph neural networks, we propose to use an incidence matrix to accurately compute the adjacency matrix of the weighted line graph, leading to dramatic reductions in computational resource usage. Experimental results on both real and simulated datasets demonstrate the effectiveness and efficiency of our proposed methods.