Emergence of weight-topology correlations in complex scale-free networks

TL;DR

This paper investigates how weight-topology correlations in scale-free networks can emerge from simple growth dynamics, introducing a weighted fitness model that exhibits phase transitions and local correlation dependence.

Contribution

It introduces a weighted fitness network model where nodes and links have intrinsic fitness, revealing how correlations can arise from basic growth rules and undergo phase transitions.

Findings

Networks with and without correlations can emerge from the same dynamics.

The model exhibits a phase transition to a state dominated by few links.

Local dependence of correlations can be controlled within the model.

Abstract

Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the node connectivities and of the link weights. A weighted fitness network is introduced in which both nodes and links are assigned intrinsic fitness. This model can show a local dependence of the weight-topology correlations and can undergo a phase transition to a state in which the network is dominated by few links which acquire a finite fraction of the total weight of the network.