A Graph-Theoretic Perspective on the Keçeci Layout: Structuring Cross-Disciplinary Inquiry

The visualization of scientific data is a fundamental step in uncovering hidden patterns and relationships within complex systems. While conventional force-directed graph layout algorithms (e.g., spring layout) are effective at displaying the general topology and clustering tendencies of systems, they possess a critical shortcoming: they are inherently non-deterministic and obscure the natural, sequential, or index-based identities of nodes. This poses a significant limitation when analysing systems that contain an intrinsic sequential logic, such as quantum circuits, metabolic pathways, crystal structures, or chronological data structures. This paper introduces the "Keçeci Layout," a deterministic and order-preserving algorithm designed to fill this analytical gap. The algorithm operates by arranging nodes sequentially along a primary axis according to their IDs, employing a predictable zigzag pattern on a secondary axis to prevent node overlaps. This approach establishes a direct and intuitive bridge between a system's abstract data structure (e.g., qubit indices, reaction steps) and its visual representation. To demonstrate the versatility and efficacy of the Keçeci Layout, four case studies from distinct scientific disciplines are presented: Chemistry, Physics, Biology, Quantum Computing, Materials Science, Molecular Biology, Computer Science, etc. In conclusion, the Keçeci Layout is proven to be a powerful scientific tool that offers analytical depth by remaining faithful to the underlying data structure, moving beyond purely aesthetic presentation. The algorithm provides a significant advantage over conventional methods, particularly for the visual analysis of ordered, hierarchical, or index-dependent systems.