Abstract:

Random networks are a fundamental tool for the analysis of large real-world structures (such as social networks, communication networks, inter-banking systems and so on) which are not directly treatable, often because of their size. The scale-free percolation random network features three properties that 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, through the statistical analysis of a dataset provided by the French Ministry of Agriculture, we verify that it encodes some relevant characteristics of the cattle trading network in France. Our final goal is to understand how an epidemic would spread on this kind of structures.