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 processes: from synchronization to the voter model
   • Examples of real-world networks
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