HySE: A Force‐Directed Layout Algorithm for Directed and Mixed Graphs

Abstract Presenting relational data in the form of graphs in a visually appealing manner can help simplify the analysis of the underlying entities and relations. Mixed graphs, comprising a central directed or hierarchical part and interconnected undirected components, offer a practical structure for representing relational data with varying levels of abstraction while managing its complexity. To comprehend the relationships in data, discover insights, and get important patterns, a well‐optimized graph layout for such graphs is needed. In response, we present HySE, a novel graph layout algorithm tailored for mixed graphs. HySE makes use of a holistic approach based on the popular force‐directed method to achieve the aesthetics and quality of an optimized force‐directed layout, not only on the undirected part of the graph but also on the hierarchy, while maintaining the cohesion between both directed and undirected elements of the graph. HySE also offers the capability to arrange graphs with solely directed relations in a hierarchical fashion, serving as a viable alternative to conventional hierarchical layout algorithms. Moreover, HySE accommodates non‐uniform node dimensions, a feature absent in traditional hierarchical layout algorithms. Experiments on randomly generated graphs confirm HySE's performance parity with state‐of‐the‐art force‐directed algorithms, maintaining quality while integrating hierarchical components into undirected graphs. HySE also matches the speed of established algorithms on small‐to‐medium‐sized graphs, ideal for interactive visual analysis tools. Implementation, documentation, and a demo page for HySE are available on GitHub as a Cytoscape.js extension [i‐Vb].