In this set of lectures, I will provide a general introduction to complex networks and to some research themes in dynamical processes on such structures. These lectures are aimed to a non-specialist audience with a minimal knowledge of probability theory. The tentative plan is: 1) Introduction: Complex networks, dynamical processes – Examples of real-world networks – Examples of processes: from synchronization to the voter model 2) Models of complex networks – The archetype: Erdos-Renyi random graph – A small-world: Watts-Strogatz – Broad degree and weight distributions: Barabasi-Albert and variants 3) Percolation and failure cascades on complex networks – Motivation – General results – Importance of the degree distribution: percolation threshold for scale-free networks 4) Epidemic spread on complex networks – Spread of diseases over contact networks; rumor spread – Spread of diseases in metapopulation models: mean-field approach; fluctuations and existence of a pandemic threshold. (Cour organisé en collaboration avec l’Ecole Doctorale de Physique de la Région Parisienne – ED 107)

IPhT