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.

The existence of anomalies is quite common, but they are hidden within the complex structure and high-dimensional node attributes of the attributed networks. As a latent hazard in existing systems, anomalies can be transformed into important instruction information once we detect them, e.g., computer network admins can react to the leakage of sensitive data if network traffic anomalies are identified. Extensive research in anomaly detection on attributed networks has proposed various techniques, which do improve the quality of data in networks, while they rarely cope with the few-shot anomaly detection problem. Few-shot anomaly detection task with only a few dozen labeled anomalies is more practical since anomalies are rare in number for real-world systems.