Dynamical Phenomena on Complex Networks

Abstract

The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used to map the Internet. Our mean-field analysis of the traceroute model provides a better understanding of the Internet topology. A second part of the thesis is devoted to the study of the weighted representation of networks and their relations with the functional properties of infrastructure systems (e.g. the airports network). Other results concerning spreading processes and percolation on weighted networks are presented. Finally, we turns to social networks, introducing the Naming Game, a model for the emergence of a communication system in a structured population of individuals. We show that the dynamical phenomena generated by this model depend strongly on the topology of the interactions.