Abstract To develop commonsense-grounded NLP applications, a comprehensive and accurate commonsense knowledge graph (CKG) is needed. It is time-consuming to manually construct CKGs and many research efforts have been devoted to the automatic construction of CKGs. Previous approaches focus on generating concepts that have direct and obvious relationships with existing concepts and lack an capability to generate unobvious concepts. In this work, we aim to bridge this gap. We propose a general graph-to-paths pretraining framework that leverages high-order structures in CKGs to capture high-order relationships between concepts. We instantiate this general framework to four special cases: long path, path-to-path, router, and graph-node-path. Experiments on two datasets demonstrate the effectiveness of our methods. The code will be released via the public GitHub repository.