In cyber security, side-channel attacks (SCA) are of interest because they target the vulnerabilities in implementation rather than inherent vulnerabilities in the algorithm. Profiled SCA is especially interesting as it assumes that the adversary has unlimited access to a clone device that can generate sufficient traces to create a profile of the device. The latest techniques used for profiled SCA are based on convolutional neural networks (CNN). However, CNN's are limited in scope in how they define convolution. By running the convolution over a graph instead, we can achieve a more flexible convolution method. Therefore, we want to apply graph neural networks (GNN) to SCA. To achieve this, we need to translate our SCA problem to a graph signal processing (GSP) problem. This is done by generating a graph based on the power traces on which the traces can be run as graph signals. Subsequently, this graph is used in a GNN to solve the GSP problem. We experiment with different GNN architectures to see how they differ in performance compared to SCA state-of-the-art. We also want to observe how our model deals with the different leakage models and if there is a considerable performance gap between them. We also want to see how GNNs deal with countermeasures such as masking and desynchronization. Finally, we perform hyper-parameter analysis to know whether we can reduce the number of learnable parameters without substantially decreasing the performance of our model. The numerical results demonstrate that our model is not competitive compared to state-of-the-art methods. The performance of our method is mainly derived from the classification multilayer perceptron instead of the graph convolutional filter layers. However, the results suggest that the graph convolutional filter layers are potentially helpful in existing SCA architecture as an initial layer that performs feature extraction.