Resource allocation (RA) has always had a prominent place in wireless communications research due to its significance for network throughput maximization, and its inherent complexity. Concurrently, graph-based solutions for RA have also grown in importance, providing opportunities for higher throughput and efficiency due to their representational capabilities, as well as challenges for realizing scalable algorithms. This article presents a comprehensive review and analysis of graph-based RA methods in three major wireless network types: cellular homogeneous and heterogeneous, device-to-device, and cognitive radio networks. The main design characteristics, as well as directions for future research, are provided for each of these categories. On the basis of this review, the concept of Graph-based Resource allocation for Integrated Space and Terrestrial communications (GRIST) is proposed. It describes the inter-connectivity and coexistence of various terrestrial and non-terrestrial networks via a hypergraph and its attributes. In addition, the implementation challenges of GRIST are explained in detail. Finally, to complement GRIST, a scheme for determining the appropriate balance between different design considerations is introduced. It is described via a simplified complete graph-based design process for resource management algorithms.