Are motorways rational from slime mould's point of view?

We analyse the results of our experimental laboratory approximation of motorway networks with slime mould Physarum polycephalum. Motorway networks of 14 geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, the Netherlands, UK and USA. For each geographical entity, we represented major urban areas by oat flakes and inoculated the slime mould in a capital. After slime mould spanned all urban areas with a network of its protoplasmic tubes, we extracted a generalised Physarum graph from the network and compared the graphs with an abstract motorway graph using most common measures. The measures employed are the number of independent cycles, cohesion, shortest paths lengths, diameter, the Harary index and the Randić index. We obtained a series of intriguing results, and found that the slime mould approximates best of all the motorway graphs of Belgium, Canada and China, and that for all entities studied the best match between Physarum and motorway graphs is detected by the Randić index (molecular branching index).