Differences between normal and shuffled texts: structural properties of weighted networks

TL;DR

This paper investigates the structural differences between real and shuffled weighted networks, revealing that certain scale-free properties are driven by Zipf's law and introducing a measure to distinguish real networks from randomized ones.

Contribution

The study demonstrates that vertex selectivity effectively differentiates real networks from shuffled counterparts and links scale-free distributions to Zipf's law in weighted networks.

Findings

Vertex selectivity distinguishes real from shuffled networks

Scale-free distributions are induced by Zipf's law

Vertex selectivity captures network correlations

Abstract

In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyse the differences between the statistical properties of a real and a shuffled network and we show that the scale free degree distribution and the scale free weight distribution are induced by the scale free strength distribution, that is Zipf's law. We test the result on a scientific collaboration network, that is a social network, and we define a measure, the vertex selectivity, that can easily distinguish a real network from a shuffled network. We prove, via an ad-hoc stochastic growing network with second order correlations, that this measure can effectively capture the correlations within the topology of the network.