KPG: Kirk representation of Power Graphs

The Kirk circle is a simple and effective method for representing power graphs and visualizing their topology. In general, nodes (buses) in an electrical network are numbered with neighboring nodes assigned consecutive or closely proximal numbers. This allows for sequential mapping of these nodes in increasing order of their numerical labels to evenly spread points on a Kirk circle. In the Kirk circle, the edge connections (branches) between nodes are indicated by straight lines (chords) between the appropriate points on the circle. The following can be easily identified when visualizing power graphs using the Kirk circle:(I) Consecutive numbering, which significantly reduces nearly diagonal chords and creates an almost empty space inside the Kirk circle;(II) Isolated vertices that are not connected to any chord;(III) Pendant vertices that are only connected to one chord;(IV) An overview of the number of edges and average degree, which are respectively represented by the total number of chords and the average chords connected to each vertex. The Kirk circle is a suitable visual method for examining the properties that power graphs possess.

柯克圆是一种简洁而有效的表示功率图并可视化其拓扑结构的方法。在一般情况下，电力网络中的节点（母线）按相邻节点的顺序或紧密相邻的数字进行编号。这允许按照数值标签的增加顺序对这些节点进行顺序映射，以均匀地分布在柯克圆上的点。在柯克圆中，节点之间的边连接（分支）通过圆上适当点之间的直线（弦）来表示。使用柯克圆可视化功率图时，以下内容可以轻易识别：（I）连续编号，这显著减少了近对角线的弦，并在柯克圆内几乎形成空白；（II）孤立顶点，这些顶点未与任何弦相连；（III）悬垂顶点，这些顶点仅与一条弦相连；（IV）边数和平均度的概览，分别由弦的总数和每个顶点连接的平均弦数表示。柯克圆是一种适合考察功率图所具有的特性的视觉方法。