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.