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

The Abdus Salam International Center for Theoretical Physics Strada Costiera 11, 34014 Trieste, Italy INFM, UdR Trieste - via Beirut 2-4, 34014, Trieste, Italy

Received: 31 May 2005
Accepted: 11 July 2005

Abstract

Different weighted scale-free networks show weight-topology correlations. A clear signature of these correlations is given by the non-linear scaling of the node strength with its connectivity. In this paper, we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the nodes connectivities and of the links 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.