Nowadays, surveillance cameras play a crucial role in maintaining security and order in public areas. To optimize their effectiveness, it is essential to have automated tools capable of detecting abnormal behavior in real-time. Previous methods often faced challenges with low-resolution video inputs and changing lighting conditions, which affect the accuracy of violence detection. Previous methods focused on accuracy and relied on a large number of model parameters. Additionally, the graph-based approach has not been extensively applied to violence detection. In this paper, we propose an effective method to detect violent behavior by leveraging the power of Graph Convolutional Networks (GCNs) from vertex and edge feature sets as inputs to the model. The proposed models, named GCNonlyEdge and GCNVertexEdge, are lightweight models that learn features from skeleton data as a graph. Therefore, the model is effective in identifying violent actions by focusing on key joints and their interactions. We experimented with these models on datasets such as HockeyFights, RWF-2000, and Violence in Movies. Our experimental results show that the GCNVertexEdge model has the best accuracy on experimental datasets, particularly on the Movie dataset. The model provides a robust solution to enhance public safety through improved surveillance systems.