The Keçeci Layout: A Deterministic, Order-Preserving Visualization Algorithm for Structured Systems

The Keçeci Layout: A Deterministic, Order-Preserving Visualization Algorithm for Structured Systems

Mehmet Keçeci

Abstract: Graph visualization is a cornerstone of network analysis, yet traditional algorithms often prioritize topological representation over the preservation of inherent node order. This can obscure sequential or procedural information critical in many scientific and structural analyses. This paper introduces the \textit{Keçeci Layout}, a deterministic, order-preserving graph layout algorithm designed to arrange nodes in a structured zigzag pattern. This method provides a clear, predictable, and structurally informative visualization for systems where the sequence of nodes is meaningful. The layout is implemented in the open-source \texttt{kececilayout} Python package, which offers seamless interoperability with major graph analysis libraries, including NetworkX, igraph, rustworkx, Networkit, and Graphillion. \texttt{kececilayout} is open source, licensed under the MIT license, and the source code is available on GitHub at \url{https://github.com/WhiteSymmetry/kececilayout}. The version of the software described in this paper is archived on Zenodo \parencite{Kececi2025m}. We detail the algorithm's methodology, showcase its implementation, and discuss its applications as a cross-disciplinary framework for structural analysis. The deterministic nature of the layout ensures that any given graph will always be rendered identically, facilitating reproducible research and comparative analysis. 

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