Subgraph counting is the problem of counting the occurrences of a given query graph in a large target graph. Large-scale subgraph counting is useful in various domains, such as motif counting for social network analysis and loop counting for money laundering detection on transaction networks. Recently, to address the exponential runtime complexity of scalable subgraph counting, neural methods are proposed. However, existing neural counting approaches fall short in three aspects. Firstly, the counts of the same query can vary from zero to millions on different target graphs, posing a much larger challenge than most graph regression tasks. Secondly, current scalable graph neural networks have limited expressive power and fail to efficiently distinguish graphs in count prediction. Furthermore, existing neural approaches cannot predict the occurrence position of queries in the target graph. Here we design DeSCo, a scalable neural deep subgraph counting pipeline, which aims to accurately predict the query count and occurrence position on any target graph after one-time training. Firstly, DeSCo uses a novel canonical partition and divides the large target graph into small neighborhood graphs. The technique greatly reduces the count variation while guaranteeing no missing or double-counting. Secondly, neighborhood counting uses an expressive subgraph-based heterogeneous graph neural network to accurately perform counting in each neighborhood. Finally, gossip propagation propagates neighborhood counts with learnable gates to harness the inductive biases of motif counts. DeSCo is evaluated on eight real-world datasets from various domains. It outperforms state-of-the-art neural methods with 137x improvement in the mean squared error of count prediction, while maintaining the polynomial runtime complexity.

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