WEIGHTED LINE GRAPH CONVOLUTIONAL NETWORKS

Abstract

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.

1. INTRODUCTION

Graph neural networks (Gori et al., 2005; Scarselli et al., 2009; Hamilton et al., 2017) have shown to be competent in solving challenging tasks in the field of network embedding. Many tasks have been significantly advanced by graph deep learning methods such as node classification tasks (Kipf & Welling, 2017; Veličković et al., 2017; Gao et al., 2018) , graph classification tasks (Ying et al., 2018; Zhang et al., 2018) , link prediction tasks (Zhang & Chen, 2018; Zhou et al., 2019) , and community detection tasks (Chen et al., 2019) . Currently, most graph neural networks capture the relationships among nodes through message passing operations. Recently, some works (Chen et al., 2019) use extra graph structures such as line graphs to enhance message passing operations in graph neural networks from different graph perspectives. A line graph is a graph that is derived from an original graph to represent connectivity between edges in the original graph. Since line graphs can encode the topology information, message passing operations on line graphs can enhance network embeddings in graph neural networks. However, graph neural networks that leverage line graph structures need to deal with two challenging issues; those are bias and inefficiency. Topology information in original graphs is encoded in line graphs but in a biased way. In particular, node features are either overstated or understated depending on their degrees. Besides, line graphs can be much bigger graphs than original graphs depending on the graph density. Message passing operations of graph neural networks on line graphs lead to significant use of computational resources. In this work, we propose to construct a weighted line graph that can correct biases in encoded topology information of line graphs. To this end, we assign each edge in a line graph a normalized weight such that each node in the line graph has a weighted degree of 2. In this weighted line graph, the dynamics of node features are the same as those in its original graph. Based on our weighted line graph, we propose a weighted line graph convolution layer (WLGCL) that performs a message passing operation on both original graph structures and weighted line graph structures. To address inefficiency issues existing in graph neural networks that use line graph structures, we further propose to implement our WLGCL via an incidence matrix, which can dramatically reduce the usage of computational resources. Based on our WLGCL, we build a family of weighted line graph convolutional networks (WLGCNs). We evaluate our methods on graph classification tasks and show that WLGCNs consistently outperform previous state-of-the-art models. Experiments on simulated data demonstrate the efficiency advantage of our implementation.

