Based on the 1981 census populations of 64 counties, lines link the centres of circles representing counties which are contiguous. Software written by the author on an Archimedes computer.
The width of the lines is in proportion to the strength of continuity (which is governed by the lengths of common boundaries). Notice that the Isle of Wight and combined Scottish islands are not connected to the mainland. The West midlands has the least neighbours of any inland area - three. Powys and North Yorkshire have the most - eight. These situations are difficult to accommodate in the cartogram. The average number of neighbours is six and that is ideal.