fundamental
properties that are often present in large real-world structures
(social networks, communication networks, inter-banking systems and so
on), but which are never present at once in classical models: (1)
Scale-free: the degree of the nodes follows a power law; (2)
Small-world: two nodes are typically at a very small graph distance;
(3) Positive clustering coefficient: two nodes with a common neighbour
have a good chance to be linked. We study a continuous version of
scale-free percolation and its possible application to the statistical
analysis of a dataset provided by the French Ministry of Agriculture.
We discuss some stochastic processes (random walks and particle
systems) on these kinds of structures with the final goal of
understanding how an epidemic would spread.