# Graph-Based Resource Allocation for Integrated Space and Terrestrial Communications
## 4 Graph-Based RA in Cellular Homogeneous and Het-Nets
### Lessons Learned and Trends in Development
The connections between these nodes (vertices of the time-varying graph) constitute the edges, which change with the fluctuation of link availability (i.e., when handover occurs). This dynamic is described by the angular parameters of the satellites' positions. RA is performed separately for the ground and space-based nodes. Link establishment that satisfies the shortest path in a graph for terrestrial, aerial and space communications is explored in [48]. The processing power and link delay between a node and the ones connected to it are considered, and they define the vertex attributes. RA is determined for specific user requirements modeled by a utility function. User pairing for NOMA has been modeled in [49] by a bipartite graph for terrestrial mobile users, the coverage of which is supplemented by a satellite node when they are outside of BS range. The channel gain between the users defines the edge attributes, and the pairing is solved via maximal matching to increase the throughput of the terrestrial BSs. _The limitation of accumulating graph topology changes in time; however, it comes from the number of vertices and connections between them, as larger graphs will require not only a more significant computational burden on each iteration, but also a more complex accumulation process._ Further development can be achieved through distributed topology generation via federated learning (FL) [50]. In addition, the implementation of the overall RA algorithm often includes several sub-problems (channel and power allocation, user grouping, handover, multiple access, etc.) that are solved independently [37; 40; 49]. Then, _the challenge is to define and solve each of them in the most computationally efficient manner using traditional optimization methods or deep learning, with respect to the essential parameters (such as the number of channels and communication nodes)._ Considering the advantage of using graph-based methods to describe the physical characteristics of the communication nodes of homogeneous and Het-Nets, their relationships, and the disadvantage of computational complexity due to allocation of many users, channels, and power levels, the review in this Section has shown that GNNs are promising for decreasing the computational load of standard heuristic optimization solutions. However, their implementation requires the following considerations: _(1) the training method involves either a preliminary simulation of the network's operation to obtain data about the nodes and their relationships (in supervised learning), or the design of a RL procedure; (2) it involves definition of the relationships between the network's nodes as components of the graph; (3) addressing MC (one UE being connected to multiple cells) and UA requires differentiation between the vertices that describe BSs and UEs; (4) attributes (such as interference levels, channel gain, associated nodes) of the vertices and edges may facilitate the learning of more complex graphs._
* Most graph-based methods in this category are evaluated for the DL case, but they may not be naturally applicable for UL communications because the interference sources (i.e., other UEs) are much greater in number than for the BSs (in the cellular Het-Net scenario). _Their transmission power is also much weaker, which needs to be considered when determining the criterion (i.e., distance) of drawing an edge between two interfering users._