Malicious software (malware) poses an increasing threat to the security of communication systems as the number of interconnected mobile devices increases exponentially. While some existing malware detection and classification approaches successfully leverage network traffic data, they treat network flows between pairs of endpoints independently and thus fail to leverage rich communication patterns present in the complete network. Our approach first extracts flow graphs and subsequently classifies them using a novel graph neural network model. We present three variants of our base model, which support malware detection and classification in supervised and unsupervised settings. We evaluate our approach on flow graphs that we extract from a recently published dataset for mobile malware detection that addresses several issues with previously available datasets. Experiments on four different prediction tasks consistently demonstrate the advantages of our approach and show that our graph neural network model can boost detection performance by a significant margin.