• Scale-free networks
• Phase Transitions
• Network Theory
• Linear Threshold Model
• Graphs
• Econophysics

The Linear Threshold Model (LTM) is a dynamic model used to describe the spreading of information on networks. In the literature, it has been applied to several kinds of (mostly simulated, sometimes real-world) networks with a simple topology.
However, it is still unclear whether the LTM can successfully modelize the behaviour of more complex networks, including many real-world cases. In my thesis, I extend the LTM to describe directed graphs. This extension is instrumental for the application of the model to networks where interactions between nodes are not symmetric. In particular, I focus on graphs which exhibit both scale-free properties and community structures. I then apply the methods developed in my thesis to study a real-world example: the payment platform of a major italian bank.