Three Essays on Dynamical Processes on Networks

Networks are an useful abstraction to model complex systems: the set of nodes represents the fundamental units, and the set of links constitutes the constraint to interactions among these units. This simple but powerful abstraction provides a framework for studying how interactions among the micro components of the system generates its macroscopic properties, or in other words for understanding the emergence of complexity. Modeling a dynamical process on a graph structure may be a hard task, and it is often necessary to implement computer simulations to study the emerging dynamics. Simulations can be very useful, and can give lots of insights about the emerging properties of a complex systembut it is always preferable to have equation based models,not necessarily as a substitute of agent based models,in fact to complement the former and give a clearer framework inside which the results of the agent based model can be better understood.