Graphs are widely used as a natural framework that captures interactions between individual elements represented as nodes in a graph. In medical applications, specifically, nodes can represent individuals within a potentially large population (patients or healthy controls) accompanied by a set of features, while the graph edges incorporate associations between subjects in an intuitive manner. This representation allows to incorporate the wealth of imaging and non-imaging information as well as individual subject features simultaneously in disease classification tasks. Previous graph-based approaches for supervised or unsupervised learning in the context of disease prediction solely focus on pairwise similarities between subjects, disregarding individual characteristics and features, or rather rely on subject-specific imaging feature vectors and fail to model interactions between them. In this paper, we present a thorough evaluation of a generic framework that leverages both imaging and non-imaging information and can be used for brain analysis in large populations. This framework exploits Graph Convolutional Networks (GCNs) and involves representing populations as a sparse graph, where its nodes are associated with imaging-based feature vectors, while phenotypic information is integrated as edge weights. The extensive evaluation explores the effect of each individual component of this framework on disease prediction performance and further compares it to different baselines. The framework performance is tested on two large datasets with diverse underlying data, ABIDE and ADNI, for the prediction of Autism Spectrum Disorder and conversion to Alzheimer's disease, respectively. Our analysis shows that our novel framework can improve over state-of-the-art results on both databases, with 70.4% classification accuracy for ABIDE and 80.0% for ADNI.