  Message passing Graph Neural Networks (GNNs) provide a powerful modeling
framework for relational data. However, the expressive power of existing GNNs
is upper-bounded by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test,
which means GNNs that are not able to predict node clustering coefficients and
shortest path distances, and cannot differentiate between different d-regular
graphs. Here we develop a class of message passing GNNs, named Identity-aware
Graph Neural Networks (ID-GNNs), with greater expressive power than the 1-WL
test. ID-GNN offers a minimal but powerful solution to limitations of existing
GNNs. ID-GNN extends existing GNN architectures by inductively considering
nodes' identities during message passing. To embed a given node, ID-GNN first
extracts the ego network centered at the node, then conducts rounds of
heterogeneous message passing, where different sets of parameters are applied
to the center node than to other surrounding nodes in the ego network. We
further propose a simplified but faster version of ID-GNN that injects node
identity information as augmented node features. Altogether, both versions of
ID-GNN represent general extensions of message passing GNNs, where experiments
show that transforming existing GNNs to ID-GNNs yields on average 40% accuracy
improvement on challenging node, edge, and graph property prediction tasks; 3%
accuracy improvement on node and graph classification benchmarks; and 15% ROC
AUC improvement on real-world link prediction tasks. Additionally, ID-GNNs
demonstrate improved or comparable performance over other task-specific graph
networks.
