Modeling real spatial networks

TL;DR

This paper analyzes transportation networks in Russia, examining their structural properties and distributions, and introduces a method to fit these properties within a nonextensive statistical framework to understand their fractal nature.

Contribution

It applies nonextensive statistics and maximum entropy principles to model degree and length distributions in real spatial networks, providing a novel approach for their analysis.

Findings

Degree and length distributions follow q-type distributions.

The method enables defining the fractal dimension of networks.

Networks exhibit properties consistent with nonextensive statistical models.

Abstract

We have studied transportation network, namely a road network of the Moscow region and airline network of the Russian Federation. We have constructed corresponding networks and studied degree distribution and length distribution for these networks, as well as the dependences on the average clustering coefficients and the nearest neighbours average degree as a function of the vertex degree. In conclusion we discuss degree and length distributions in the framework of the nonextensive statistics, using the maximum entropy approach and the model with additive and multiplicative noise. We present a procedure of fitting the results of the data processing to the q-type distribution which allows the fractal dimension definition of the networks under study.