In an era where efficient processing of complex graph structures is increasingly vital across various domains, such as social networks and biological system modeling, there arises a need for robust computational architectures. This Kolloquium introduces a novel approach that incorporates a higher-order pipeline architecture, aiming to enhance graph data processing. Integrating functional programming with object-oriented principles facilitates complex data processing through an intuitive, modular system. Central to this system is the notion of treating computation units as first-class entities, which promotes modular and type-safe environments. Additionally, the system includes a higher-order traversal abstraction to support flexible data manipulation strategies, a directed data-transfer protocol for efficient data flow management, and an operator model that enhances the robust lifecycle management of operations. The adaptability and performance of this system are further augmented by its capability to incorporate various graph computation models, such as vertex-centric and edge-centric processing. This approach contributes to scalable solutions that meet diverse computational needs without overcomplicating the user interface by offering a structured yet adaptable method for graph data handling.