[IMPORTANT UPDATE] There was an incorrect ground-truth labeling for raw data "./data/count_graphlet/raw/data.mat" in the version before 2023/3/17. We corrected the labels in this repo and updated our experimental results. Sorry for any inconvenience and confusion.
This repository contains the official code for the paper Boosting the Cycle Counting Power of Graph Neural Networks with I $^2$-GNNs.
Message Passing Neural Networks (MPNNs) are a widely used class of Graph Neural Networks (GNNs). The limited representational power of MPNNs inspires the study of provably powerful GNN architectures. However, knowing one model is more powerful than another gives little insight about what functions they can or cannot express. It is still unclear whether these models are able to approximate specific functions such as counting certain graph substructures, which is essential for applications in biology, chemistry and social network analysis. Motivated by this, we propose to study the counting power of Subgraph MPNNs, a recent and popular class of powerful GNN models that extract rooted subgraphs for each node, assign the root node a unique identifier and encode the root node’s representation within its rooted subgraph. Specifically, we prove that Subgraph MPNNs fail to count more-than-4-cycles at node level, implying that node representations cannot correctly encode the surrounding substructures like ring systems with more than four atoms. To overcome this limitation, we propose I2-GNNs to extend Subgraph MPNNs by assigning different identifiers for the root node and its neighbors in each subgraph. I2- GNNs’ discriminative power is shown to be strictly stronger than Subgraph MPNNs and partially stronger than the 3-WL test. More importantly, I2-GNNs are proven capable of counting all 3, 4, 5 and 6-cycles, covering common substructures like benzene rings in organic chemistry, while still keeping linear complexity. To the best of our knowledge, it is the first linear-time GNN model that can count 6-cycles with theoretical guarantees. We validate its counting power in cycle counting tasks and demonstrate its competitive performance in molecular prediction benchmarks.
The following dependencies are required for this project:
- python 3.9.12
- pytorch 1.11.0
- pytorch gemetric (pyg) 2.0.4
- tqdm 4.64.0
- networkx 2.8.2
- rdkit 2022.03.2
- ogb 1.3.3
- dgl 0.9.0
This part empirically evaluates the stronger counting power of I2-GNNs compared to other subgraph GNNs.
To reproduce the counting results of I2-GNNs (Table 2, 3 in the paper), run
bash run_count.sh I2GNN
to execute training and test on all cycles and graphlets mentioned in the paper. Replace parameter "I2GNN" with "NGNN", "IDGNN", "GNNAK", "PPGN" and "GNN" to get the results for other baseline models.
To reproduce the results of I2-GNN on QM9 (Table 4 in the paper), run:
bash run_qm9.sh
to execute training and test on all 12 targets of QM9.
Download ZINC dataset and ZINC-full dataset and save under "data/zinc/raw" and "data/zinc-full/raw" respectively.
To reproduce the results of I2-GNN on ZINC (Table 5 in the paper), run:
bash run_zinc.sh zinc
To reproduce the results of I2-GNN on ZINC-full (Table 5 in the paper), run:
bash run_zinc.sh zinc-full
To reproduce the results of I2-GNN on ogb-molhiv (Table 5 in the paper), run:
bash run_hiv.sh
https://arxiv.org/abs/2210.13978
@article{huang2022boosting,
title={Boosting the Cycle Counting Power of Graph Neural Networks with I $\^{} 2$-GNNs},
author={Huang, Yinan and Peng, Xingang and Ma, Jianzhu and Zhang, Muhan},
journal={arXiv preprint arXiv:2210.13978},
year={2022}
}
If you have any question about the code, please feel free to contact Yinan Huang ([email protected])!