Recent advancements in neuroimaging data analysis facilitate the characterization of adaptive changes in brain network integration. This study introduces a distinctive approach that merges knowledge-informed and data-driven methodologies, offering a nuanced way to more effectively understand these changes. Utilizing graph network analysis, along with existing neurobiological knowledge of domain-specific brain network systems, we uncover a deeper understanding of brain network interaction and integration. As a proof of concept, we applied our approach to the language domain, a well-known large-scale network system as a representative model system, using functional imaging datasets with specific language tasks for validation of our proposed approach. Our results revealed a double dissociation between motor and sensory language modules during word generation and comprehension tasks. Furthermore, by introducing a hierarchical nature of brain networks and introducing local and global metrics, we demonstrated that hierarchical levels of networks exhibit distinct ways of integration of language brain networks. This innovative approach facilitates a differentiated and thorough interpretation of brain network function in local and global manners, marking a significant advancement in our ability to investigate adaptive changes in brain network integration in health and disease. Author Summary This study introduces a novel approach combining knowledge-informed and data-driven methodologies to analyze adaptive changes in brain network integration. By integrating graph network analysis with existing neurobiological knowledge of domain-specific brain networks, we provide deeper insights into brain network interaction, coordination, and integration. Using the language domain as a model system and functional imaging data from specific language tasks, our approach reveals a double dissociation between motor and sensory language modules during word generation and comprehension tasks. By analyzing hierarchical networks at multiple levels and introducing local and global metrics, we demonstrate that hierarchical levels of networks exhibit distinct integration patterns. This method surpasses conventional regional activation analysis, offering a significant advancement in investigating adaptive changes in brain network integration in health and disease.