Graph Classification with Minimum DFS Code: Improving Graph Neural Network Expressivity

Abstract

Graph neural networks (GNNs) generally follow a recursive neighbors aggregation scheme. Recent GNNs are not powerful than the 1-Weisfeiler Lehman test, which is a necessary but insufficient condition for graph isomorphism, hence limiting their abilities to utilize graph structures properly. Moreover, deep GNNs with many convolutional layers suffer from over-smoothing, thus cannot capture long-range dependencies. As a result, downstream applications, such as graph classification, are impacted. To this end, we design GNNs on top of the minimum DFS code, which is a canonical form of a graph, and being injective it captures the graph structure precisely along with node and edge labels. Due to the sequential structure of the minimum DFS code, we employ state-of-the-art RNNs (LSTM, BiLSTM, GRU) and Transformer-based sequence classification techniques. While one can compute the minimum DFS code efficiently in practice, LSTM, BiLSTM, GRU, and Transformers capture long-term dependencies in arbitrary length sequences. We also consider a novel variant of the minimum DFS code, which is not injective, but it reduces the complexity of the feature space, increases generalizability, and also improves the classification performance over many real-world graph datasets. Our thorough empirical comparisons with six real-world network datasets demonstrate the accuracy and efficiency of our methods. We have open-sourced our solution framework [17] in which one can plug in different graph datasets and get their classification results. This will benefit researchers and practitioners, biologists, social scientists, and data scientists, among others. © 2021 IEEE.