Pretrained language models are expected to effectively map input text to a set of vectors while preserving the inherent relationships within the text. Consequently, designing a white-box model to compute metrics that reflect the presence of specific internal relations in these vectors has become a common approach for post-hoc interpretability analysis of pretrained language models. However, achieving interpretability in white-box models and ensuring the rigor of metric computation becomes challenging when the source model lacks inherent interpretability. Therefore, in this paper, we discuss striking a balance in this trade-off and propose a novel line to constructing metrics for understanding the mechanisms of pretrained language models. We have specifically designed a family of metrics along this line of investigation, and the model used to compute these metrics is referred to as the tree topological probe. We conducted measurements on BERT-large by using these metrics. Based on the experimental results, we propose a speculation regarding the working mechanism of BERT-like pretrained language models, as well as a strategy for enhancing fine-tuning performance by leveraging the topological probe to improve specific submodules.