A Summary of Results on Mean Distance in Shapes
John Kevin Doyle, Jack E. Graver · Environment and Planning B Planning and Design · 1982
The average or mean of the distances between pairs of vertices in a connected graph is a natural measure of the compactness of that graph. Using graphs to represent shapes, or corridor arrangements, we arrive, through a limiting process, at a concept for mean distance in shapes. This paper gives the mean distance for eight specific shapes and six infinite families of shapes.