Aim of the course

A network is a set of agents pairwise connected by links. Despite the simplicity of this definition, the theoretical properties of networks are extremely rich and diversified. Most notably, networks turn out to be extremely flexible in modelling a broad variety of phenomena characterized by a large number of interconnected elementary units: social networks, the Internet and the WWW, sensor networks, ecological communities, biochemical systems, energy transportation networks, economic and financial networks, are just but a few examples. Since networks permeate almost every conceivable discipline, the study of “network science” is becoming a crucial component of modern scientific education. The course is aimed at illustrating the fundamental theoretical notions as well as a number of applications in specific fields.

Program

Complex networks (structural properties):

• Distance, diameter, clustering, degree distribution
• Network models: random, scale-free, small-world
• Centrality measures: closeness, betweenness, PageRank
• Community and core-periphery analysis
• Robustness: resilience and tolerance to failure

Dynamical systems on networks:

• Robustness: failure cascades
• Spreading processes in networks
• Networks of dynamical systems
• Collective dynamics: consensus and synchronization

Seminars on network modelling and analysis in specific application fields (final list to be confirmed):

• WWW and social media
• Economics and finance
• Epidemiology
• Resilience of strategic infrastructures

The student will prepare a written report or an oral presentation (with slides) of a topic (paper, book chapter, etc) assigned by the teacher.

October 6, 2020, 9.00-13.30: Complex networks (structural properties) (1)
October 7, 2020, 9.00-13.00: Complex networks (structural properties) (2)
October 8, 2020, 9.00-13.30: Complex networks (structural properties) (3) - Dynamical systems on networks (1)
October 13, 2020, 9.00-13.00: Dynamical systems on networks (2)
October 14, 2020, 9.00-13.00: Seminars (1)
October 15, 2020, 9.00-13.00: Seminars (2)