While graph convolution based methods have become the de-facto standard for graph representation learning, their applications to disease prediction tasks remain quite limited, particularly in the classification of neurodevelopmental and neurodegenerative brain disorders. In this paper, we introduce an aggregator normalization graph convolutional network by leveraging aggregation in graph sampling, as well as skip connections and identity mapping. The proposed model learns discriminative graph node representations by incorporating both imaging and non-imaging features into the graph nodes and edges, respectively, with the aim of augmenting predictive capabilities and providing a holistic perspective on the underlying mechanisms of brain disorders. Skip connections enable the direct flow of information from the input features to later layers of the network, while identity mapping helps maintain the structural information of the graph during feature learning. We benchmark our model against several recent baseline methods on two large datasets, Autism Brain Imaging Data Exchange (ABIDE) and Alzheimer's Disease Neuroimaging Initiative (ADNI), for the prediction of autism spectrum disorder and Alzheimer's disease, respectively. Experimental results demonstrate the competitive performance of our approach in comparison with recent baselines in terms of several evaluation metrics, achieving relative improvements of 50% and 13.56% in classification accuracy over graph convolutional networks on ABIDE and ADNI, respectively.