Modeling the evolution of weighted networks

Alain Barrat, Marc Barthélemy, Alessandro Vespignani
2004 Physical Review E  
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and non-linearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical
more » ... the statistical properties observed in several real-world systems. In particular, the model yields a non-trivial time evolution of vertices properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree.
doi:10.1103/physreve.70.066149 pmid:15697476 fatcat:rb4edapih5bgpg2p6zmlsvgjpe