  Linear Graph Convolutional Networks (GCNs) are used to classify the node in
the graph data. However, we note that most existing linear GCN models perform
neural network operations in Euclidean space, which do not explicitly capture
the tree-like hierarchical structure exhibited in real-world datasets that
modeled as graphs. In this paper, we attempt to introduce hyperbolic space into
linear GCN and propose a novel framework for Lorentzian linear GCN.
Specifically, we map the learned features of graph nodes into hyperbolic space,
and then perform a Lorentzian linear feature transformation to capture the
underlying tree-like structure of data. Experimental results on standard
citation networks datasets with semi-supervised learning show that our approach
yields new state-of-the-art results of accuracy 74.7$\%$ on Citeseer and
81.3$\%$ on PubMed datasets. Furthermore, we observe that our approach can be
trained up to two orders of magnitude faster than other nonlinear GCN models on
PubMed dataset. Our code is publicly available at
https://github.com/llqy123/LLGC-master.
