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

TL;DR

This study uses slime mould Physarum polycephalum to experimentally approximate and analyze the structure of motorway networks across various countries, revealing similarities and differences through graph comparison measures.

Contribution

It introduces a novel biological approach to model and compare motorway networks using slime mould experiments and graph analysis.

Findings

Slime mould best approximates Belgian, Canadian, and Chinese motorway networks.

The Randic index effectively measures the similarity between Physarum and motorway graphs.

Physarum networks show intriguing structural similarities to real-world motorways.

Abstract

We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, The Netherlands, UK, 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 Randic 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 Randic index (molecular branching index).