Anomaly detection is a challenge well-suited to machine learning and in the context of information security, the benefits of unsupervised solutions show significant promise. Recent attention to Graph Neural Networks (GNNs) has provided an innovative approach to learn from attributed graphs. Using a GNN encoder-decoder architecture, anomalous edges between nodes can be detected during the reconstruction phase. The aim of this research is to determine whether an unsupervised GNN model can detect anomalous network connections in a static, attributed network. Network logs were collected from four corporate networks and one artificial network using endpoint monitoring tools. A GNN-based anomaly detection system was designed and employed to score and rank anomalous connections between hosts. The model was validated against four realistic experimental scenarios against the four large corporate networks and the smaller artificial network environment. Although quantitative metrics were affected by factors including the scale of the network, qualitative assessments indicated that anomalies from all scenarios were detected. The false positives across each scenario indicate that this model in its current form is useful as an initial triage, though would require further improvement to become a performant detector. This research serves as a promising step for advancing this methodology in detecting anomalous network connections. Future work to improve results includes narrowing the scope of detection to specific threat types and a further focus on feature engineering and selection.