Multifractal approach for comparing road transport network geometry: The case of Spain

Spain is a highly decentralized country composed of 17 autonomous communities (regional political and administrative territories), where the power is divided between the central government and a limited self-government of the communities. In the case of the road network, the competences are not completely delegated but the management and planning of its roads are shared between the central state and the communities. This dual management has led to asymmetries in the road networks of the different autonomous communities that have not been characterized yet. Its complex geometry and the different size of the territories make difficult both, the characterization of each network, as well as the comparison between the road networks of the different territories. Multifractal analysis is a robust tool that allows to summarizing characteristic parameters of the network structures. One of its main features is that the results obtained from this analysis are independent of the scale. The sandbox algorithm has been extensively used for the estimation of the dimension function, D (q), because of the adequate construction of the entirely generalized dimension function and for avoiding the undesirable “border effects”. In this work, we are applying the sandbox algorithm for characterizing the Spanish road network. This study shows that road networks exhibit a multifractal behaviour depending on the contribution of underlying subnetworks. In order to measure the contribution of these subnetworks we have also performed a multifractal analysis taking into account two different approaches: the ownership and the capacity of the road. Results also suggest that Spanish road network has a remarkably tendency to fractality with a fractal dimension around 1.8. However, this behaviour is not identical in all autonomous communities. Considering that multifractal parameters are independent of the scale, we were able to group the road networks with similar multifractal structures in the autonomous communities' networks, through a cluster analysis.