The expressive power of message passing GNNs is upper-bounded by Weisfeiler-Lehman (WL) test. To achieve high expressive GNNs beyond WL test, we propose a novel graph isomorphism test method, namely Twin-WL, which simultaneously passes node labels and node identities rather than only passes node label as WL. The identity-passing mechanism encodes complete structure information of rooted subgraph, and thus Twin-WL can offer extra power beyond WL at distinguishing graph structures. Based on Twin-WL, we implement two Twin-GNNs for graph classification via defining readout function over rooted subgraph: one simply readouts the size of rooted subgraph and the other readouts rich structure information of subgraph following a GNN-style. We prove that the two Twin-GNNs both have higher expressive power than traditional message passing GNNs. Experiments also demonstrate the Twin-GNNs significantly outperform state-of-the-art methods at the task of graph classification.
@article{arxiv.2203.11683,
title = {Twin Weisfeiler-Lehman: High Expressive GNNs for Graph Classification},
author = {Zhaohui Wang and Qi Cao and Huawei Shen and Bingbing Xu and Xueqi Cheng},
journal= {arXiv preprint arXiv:2203.11683},
year = {2022}
}