  As an emerging artificial intelligence technology, graph neural networks
(GNNs) have exhibited promising performance across a wide range of
graph-related applications. However, information exchanges among neighbor nodes
in GNN pose new challenges in the resource-constrained scenario, especially in
wireless systems. In practical wireless systems, the communication links among
nodes are usually unreliable due to wireless fading and receiver noise,
consequently resulting in performance degradation of GNNs. To improve the
learning performance of GNNs, we aim to maximize the number of long-term
average (LTA) communication links by the optimized power control under energy
consumption constraints. Using the Lyapunov optimization method, we first
transform the intractable long-term problem into a deterministic problem in
each time slot by converting the long-term energy constraints into the
objective function. In spite of this non-convex combinatorial optimization
problem, we address this problem via equivalently solving a sequence of convex
feasibility problems together with a greedy based solver. Simulation results
demonstrate the superiority of our proposed scheme over the baselines.
