  Small satellite networks (SSNs), which are constructed by large number of
small satellites in low earth orbits (LEO), are considered as promising ways to
provide ubiquitous Internet access. To handle stochastic Internet traffic,
on-board routing is necessary in SSNs. However, large-scale, high dynamic SSN
topologies and limited resources make on-board routing in SSNs face great
challenges. To address this issue, we turn to graph neural network (GNN), a
deep learning network inherently designed for graph data, motivated by the fact
that SSNs can be naturally modeled as graphs. By exploiting GNN's topology
extraction capabilities, we propose a GNN-based learning routing approach (GLR)
to achieve near-optimal on-board routing with low complexity. We design
high-order and low-order feature extractor and cross process to deal with high
dynamic topologies of SSNs, even those topologies that have never been seen in
training. Simulation results demonstrate that GLR results in a significant
reduction in routing computation cost while achieves near-optimal routing
performance in SSNs with different scales compared with typical existing
satellite routing algorithms.
