To unravel the mechanism of immune activation and suppression within tumors, a critical step is to identify transcriptional signals governing cell-cell communication between tumor and immune/stromal cells in the tumor microenvironment. Central to this communication are interactions between secreted ligands and cell-surface receptors, creating a highly connected signaling network among cells. Recent advancements in in situ-omics profiling, particularly spatial transcriptomic (ST) technology, provide unique opportunities to directly characterize ligand-receptor signaling networks that power cell-cell communication. In this paper, we propose a novel statistical method, LRnetST, to characterize the ligand-receptor interaction networks between adjacent tumor and immune/stroma cells based on ST data. LRnetST utilizes a directed acyclic graph model with a novel approach to handle the zero-inflated distributions of ST data. It also leverages existing ligand-receptor regulation databases as prior information, and employs a bootstrap aggregation strategy to achieve robust network estimation. Application of LRnetST to ST data of high-grade serous ovarian tumor samples revealed both common and distinct ligand-receptor regulations across different tumors. Some of these interactions were validated through both a MERFISH dataset and a CosMx SMI dataset of independent ovarian tumor samples. These results cast light on biological processes relating to the communication between tumor and immune/stromal cells in ovarian tumors. An open-source R package of LRnetST is available on GitHub at https://github.com/jie108/LRnetST.