Graph-structured data provide an integrated description of complex systems, encompassing not only the interactions among nodes, but also the intrinsic features that characterize these nodes. These features play a fundamental role in the formation of links within the network, making them valuable for extracting meaningful information. In this paper, we present a comprehensive framework that treats features as tangible entities and establishes a bipartite graph connecting nodes and features. By assuming that nodes sharing similarities should also share features, we introduce a hyperbolic geometric space where both nodes and features coexist, shaping the structure of both the node network and the bipartite network of nodes and features. Through this framework, we can identify correlations between nodes and features in real data and generate synthetic datasets that mimic the topological properties of their connectivity patterns. Notably, node features are at the core of deep learning techniques, such as graph convolutional neural networks (GCNs), offering great utility in downstream tasks. Therefore, our approach provides insights into the inner workings of GCNs by revealing the intricate structure of the data.