Hive plots are a graph visualization style placing vertices on a set of radial axes emanating from a common center and drawing edges as smooth curves connecting their respective endpoints. In previous work on hive plots, assignment to an axis and vertex positions on each axis were determined based on selected vertex attributes and the order of axes was prespecified. Here, we present a new framework focusing on combinatorial aspects of these drawings to extend the original hive plot idea and optimize visual properties such as the total edge length and the number of edge crossings in the resulting hive plots. Our framework comprises three steps: (1) partition the vertices into multiple groups, each corresponding to an axis of the hive plot; (2) optimize the cyclic axis order to bring more strongly connected groups near each other; (3) optimize the vertex ordering on each axis to minimize edge crossings. Each of the three steps is related to a well-studied, but NP-complete computational problem. We combine and adapt suitable algorithmic approaches, implement them as an instantiation of our framework and show in a case study how it can be applied in a practical setting. Furthermore, we conduct computational experiments to gain further insights regarding algorithmic choices of the framework. The code of the implementation and a prototype web application can be found on OSF.

翻译：蜂房图是一种图可视化风格，将顶点放置在一组从共同中心辐射的径向轴上，并以平滑曲线绘制连接其各自端点的边。在先前关于蜂房图的研究中，顶点分配到哪条轴以及每条轴上的顶点位置是基于选定的顶点属性确定的，且轴的顺序是预先指定的。本文提出了一种新框架，重点研究这些绘图的组合方面，以扩展原始蜂房图思想，并优化最终蜂房图中的总边长和边交叉数等视觉属性。我们的框架包括三个步骤：（1）将顶点划分为多个组，每组对应蜂房图中的一条轴；（2）优化循环轴顺序，使连接更紧密的组彼此靠近；（3）优化每条轴上的顶点顺序，以最小化边交叉。这三个步骤中的每一步都对应一个已被充分研究但属于NP完全的计算问题。我们结合并改编了合适的算法方法，将其作为框架的一个实例实现，并通过案例研究展示其在实际场景中的应用。此外，我们进行了计算实验，以进一步了解框架中算法选择的优劣。实现代码和原型Web应用程序可在OSF上获取。