Detecting cyberattacks using Graph Neural Networks (GNNs) has seen promising results recently. Most of the state-of-the-art models that leverage these techniques require labeled examples, hard to obtain in many real-world scenarios. To address this issue, unsupervised learning and Self-Supervised Learning (SSL) have emerged as interesting approaches to reduce the dependency on labeled data. Nonetheless, these methods tend to yield more anomalous detection algorithms rather than effective attack detection systems. This paper introduces Few Edges Are Enough (FEAE), a GNN-based architecture trained with SSL and Few-Shot Learning (FSL) to better distinguish between false positive anomalies and actual attacks. To maximize the potential of few-shot examples, our model employs a hybrid self-supervised objective that combines the advantages of contrastive-based and reconstruction-based SSL. By leveraging only a minimal number of labeled attack events, represented as attack edges, FEAE achieves competitive performance on two well-known network datasets compared to both supervised and unsupervised methods. Remarkably, our experimental results unveil that employing only 1 malicious event for each attack type in the dataset is sufficient to achieve substantial improvements. FEAE not only outperforms self-supervised GNN baselines but also surpasses some supervised approaches on one of the datasets.