Efficient and Accurate Subgraph Counting: A Bottom-up Flow-learning Based Approach

Subgraph counting is a fundamental problem in graph analytics with broad applications, yet remains computationally intractable due to its #P-hardness. To address this, numerous approximate solutions have been proposed, though they often suffer from limited efficiency and accuracy. In this paper, we introduce FlowSC, a novel approach that achieves both high accuracy and efficiency in subgraph counting. Our method starts with an enhanced candidate filtering algorithm, which significantly improves the pruning capability of bipartite graph-based techniques with minimal overhead. Building on this, we propose a bottom-up flow-learning model based on a new Graph Neural Network (GNN) architecture. By employing a carefully designed message-passing mechanism, the model explicitly controls the direction, range, and iterations of information flow, enabling a simulation of the candidate tree-based counting process. This mechanism is further empowered by a customized message aggregation technique, alongside a pretraining strategy that facilitates model training. Extensive experiments show that FlowSC can achieve up to 4 orders of magnitude improvement in accuracy and 3× improvement in efficiency over the baselines across datasets, while scaling to billion-edge graphs.