Graph structure reforming framework enhanced by commute time distance for graph classification

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As a graph data mining task, graph classification has high academic value and wide practical application. Among them, the graph neural network-based method is one of the mainstream methods. Most graph neural networks (GNNs) follow the message passing paradigm and can be called Message Passing Neural Networks (MPNNs), achieving good results in structural data-related tasks. However, it has also been reported that these methods suffer from over-squashing and limited expressive power. In recent years, many works have proposed different solutions to these problems separately, but none has yet considered these shortcomings in a comprehensive way. After considering these several aspects comprehensively, we identify two specific defects: information loss caused by local information aggregation, and an inability to capture higher-order structures. To solve these issues, we propose a plug-and-play framework based on Commute Time Distance (CTD), in which information is propagated in commute time distance neighborhoods. By considering both local and global graph connections, the commute time distance between two nodes is evaluated with reference to the path length and the number of paths in the whole graph. Moreover, the proposed framework CTD-MPNNs (Commute Time Distance-based Message Passing Neural Networks) can capture higher-order structural information by utilizing commute paths to enhance the expressive power of GNNs. Thus, our proposed framework can propagate and aggregate messages from defined important neighbors and model more powerful GNNs. We conduct extensive experiments using various real-world graph classification benchmarks. The experimental performance demonstrates the effectiveness of our framework. Codes are released on https://github.com/Haldate-Yu/CTD-MPNNs.