3D scene graph generation (3DSGG), which involves classifying objects and predicates, is an emerging topic in 3D scene understanding. Recent studies leveraging graph neural networks (GNNs) have introduced sophisticated architectures that enhance classification performance. However, since GNNs serve as the core and constitute the majority of parameters in 3DSGG models, their computational demands substantially increase overall complexity, which makes it difficult to determine the optimal model capacity. In this paper, we propose the first compression framework for lightweight 3DSGG models, based on pruning-as-search and knowledge distillation. This framework integrates multiple strategies and modules. In phase 1, the framework identifies the optimal compression ratio through pruning-as-search. In phase 2, to mitigate the accuracy loss incurred during compression, we employ structured pruning and a novel knowledge distillation strategy that effectively transfers precise information from the teacher to the compressed model. Experimental results show that our approach reduces model size by more than half while improving classification accuracy. Code is available athttps://github.com/hojunking/3DSGG-compression.