Graph-structured data is vital for modeling complex systems, and graph neural networks (GNNs) have become essential in graph machine learning for applications like recommendation systems and drug discovery. However, GNNs require rich data, often lacking in practical scenarios due to collection and annotation difficulties. This thesis aims to enhance GNNs' capabilities with limited information. It introduces novel GNN models for handling insufficient data and presents solutions for real-world applications, such as anomaly detection and out-of-distribution detection. This research advances GNN robustness and applicability, fostering the development of more powerful graph machine learning models.