Anomaly detection in network data is a critical task in various domains, and graph-based approaches, particularly Graph Convolutional Networks (GCNs), have gained significant attention in recent years. This paper provides a comprehensive analysis of anomaly detection techniques, focusing on the importance and challenges of network anomaly detection. It introduces the fundamentals of GCNs, including graph representation, graph convolutional operations, and the graph convolutional layer. The paper explores the applications of GCNs in anomaly detection, discussing the graph convolutional layer, hierarchical representation learning, and the overall process of anomaly detection using GCNs. A thorough review of the literature is presented, with a comparative analysis of GCNbased approaches. The findings highlight the significance of graph-based techniques, deep learning, and various aspects of graph representation in anomaly detection. The paper concludes with a discussion on key insights, challenges, and potential advancements, such as the integration of deep learning models and dynamic graph analysis.