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（Kirk circle）是用于表征电力网络图并可视化其拓扑结构的简便高效方法。一般而言，电力网络中的节点（母线）会进行编号，且相邻节点被分配连续或彼此紧邻的编号。这使得我们可以将这些节点按照编号升序依次映射至柯克圆上均匀分布的点位。在柯克圆中，节点间的边连接（支路）通过圆周上对应点位间的直线（弦）来表示。借助柯克圆可视化电力网络图时，可轻松识别以下特征：(I) 连续编号规则：该规则可大幅减少近似对角弦，并在柯克圆内部形成近乎空旷的区域；(II) 孤立顶点：未与任何弦相连的顶点；(III) 悬垂顶点：仅与一条弦相连的顶点；(IV) 边数与平均度概览：二者分别对应总弦数与每个顶点连接的平均弦数。柯克圆是用于探究电力网络图固有属性的适配可视化方法。