DeSCo: Towards Generalizable and Scalable Deep Subgraph Counting

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 analysis for social network and loop counting for money laundering detection. Recently, to address the exponential runtime complexity of scalable subgraph counting, neural methods are proposed. However, existing approaches fall short in three aspects. Firstly, the subgraph counts vary from zero to millions for different graphs, posing a much larger challenge than regular graph regression tasks. Secondly, current scalable graph neural networks have limited expressive power and fail to efficiently distinguish graphs for count prediction. Furthermore, existing neural approaches cannot predict query occurrence positions.

We introduce DeSCo, a scalable neural deep subgraph counting pipeline, designed to accurately predict both the count and occurrence position of queries on target graphs post single training. Firstly, DeSCo uses a novel canonical partition and divides the large target graph into small neighborhood graphs, greatly reducing the count variation while guaranteeing no missing or double-counting. Secondly, neighborhood counting uses an expressive subgraph-based heterogeneous graph neural network to accurately count 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 137× improvement in the mean squared error of count prediction, while maintaining the polynomial runtime complexity. Our open-source project is at https://github.com/fuvty/DeSCo.