The pencil-metric is an experimental metric to compare layout-algorithms in "real" usecases. Therefore the height and width of a graph will be measured after the layout is done for a general, not bounded area. To match the given area, like an Din A4 sheet, a 10:16 screen or a simple square the total graph has to be scaled with the same factor (at least in KLay Layered). Since all nodes are layered with their real width, this scale provides a reason how big the components of the graph can be. The pencil-metric defines this scaling factor as min(rh/h,rw/w) , where h and w are the measured height and width after the layering and rh and rw are the reference height and width of the chosen usecase. For the 10:16 example two possible values would be: rh = 1920 rw=1200.
Motivation
The goals of automated graph layout is to generate or improve graphs in a way that the user can get the most important informations with the first quick view.
Besides other criteria to examine and compare the readability of a graph, like the number of edge-crossings, an important role is the actual size of the displayed graph.A graph can be easily downscaled if it is to big, but the other way around would need more space or a restriction which part of the graph should be displayed. So we consider an algorithm that creates a graph with a bigger scale superior to another with a lesser scale.
To determine this criteria in our meetings, a pencil was often used, to see if a node would cover more or less twith the compared algorithms.
We don't think that this metric can solely measure the readability of a Graph, but that it is an important factor and especially describes the effective area-usage of the algorithms.
Example Results for 10:16