Water is the lifeblood of river networks, and its quality plays a crucial role in sustaining both aquatic ecosystems and human societies. Real-time monitoring of water quality is increasingly reliant on in-situ sensor technology. Anomaly detection is crucial for identifying erroneous patterns in sensor data, but can be a challenging task due to the complexity and variability of the data, even under normal conditions. This paper presents a solution to the challenging task of anomaly detection for river network sensor data, which is essential for accurate and continuous monitoring. We use a graph neural network model, the recently proposed Graph Deviation Network (GDN), which employs graph attention-based forecasting to capture the complex spatio-temporal relationships between sensors. We propose an alternate anomaly scoring method, GDN+, based on the learned graph. To evaluate the model's efficacy, we introduce new benchmarking simulation experiments with highly-sophisticated dependency structures and subsequence anomalies of various types. We further examine the strengths and weaknesses of this baseline approach, GDN, in comparison to other benchmarking methods on complex real-world river network data. Findings suggest that GDN+ outperforms the baseline approach in high-dimensional data, while also providing improved interpretability. We also introduce software called gnnad.