PhD school on Network Science, University of Pisa, 2015
Network science (aka the science of Complex Networks) has emerged in the last ten years as an inter-disciplinary and yet distinct research field, seeking to discover common principles, algorithms and tools that govern networks as different as the Internet, the web, human social networks, gene regulatory networks, the brain, ecosystems, social organizations, transport networks.
Teacher: Giovanni Neglia
Easley and Kleinberg, Networks, Crowds and Markets (a pre-publication draft of the book is available here)
Barrat, Barthélemy and Vespignani, Dynamical Processes on Complex Networks
Moez Draief and Laurent Massoulié, Epidemics and Rumours in Complex Networks, an early draft is available here
You can freely use the slides below for your presentations, but I would like to be informed and please acknowledge the source in your presentation. Any comment is welcome.
First lesson (March 23, 2015): In this lesson we introduce the different definitions of complex networks and we question if network science is really a new science. We look at different topological properties usually present in complex networks (small diameters, high clustering, heavy-tailed degree distribution) and we present some random graph models that explain how these properties can arise. Slides. We also introduce Galton Watson branching process and study its extinction probability. References: sections 21.1-2 of Easley&Kleinberg, sections 1.1-4 of Draief&Massoulié or chapter 2 of their draft.
Second lesson (March 24, 2015): In this lesson we study some phase transitions exhibited by Erdös-Rényi (emergence of the giant component, of connectivity, of logarithmic diameter) and their relation with Galton Watson branching processes. References: chapters 2, 3, and 4 of Draief&Massoulié or chapters 3, 4, and 5 of their draft.
Third lesson (March 25, 2015): In this lesson we introduce some of the software tools to process graphs. Slides.
Fourth lesson (March 26, 2015): In this lesson we present Albert-Barabasi model for random power law networks and we discuss when and how is possible to navigate in complex networks. Slides. References: section 6.3 of Draief&Massoulié or of the draft.
Fifth lesson (March 27, 2015): In this lesson we continue our study of epidemics (references: Sections 27.3-27.6 of Easley and Kleinberg, Networks, Crowds and Markets, Sections 9.1-9.2 of Barrat, Barthélemy and Vespignan), describe Twitter graph (Slides) and how to maximize our influence in Twitter (Slides).
First assignment, deadline March 23 2015, watch the documentary How Kevin Bacon Cured Cancer and send to the teacher an email with 2 questions rising from the movie you would like the course to address. An alternative lower quality video is here.
Second assignment, deadline March 25 2015, follow the instructions here.