Network science, expanding rapidly within the last few decades, has been causing a major paradigm shift in the way science is being done in the 21st century. It provides the concepts and tools to help us understand various complex systems in nature, society and technology from a viewpoint of connection and interaction. Topics range from the way cells function and create living things, to the ways neurons connect and configure the way brains and minds work, to the ways a disease spreads through social contacts and transportation channels. It has become an essential body of knowledge for scientific research in a wide variety of fields, including engineering, physics, computer science, biology, medicine, and social/organizational sciences.

This course provides students with concepts and mathematical/computational tools developed in network science, for modeling, analyzing and simulating the structures and dynamics of various complex networks. Specific topics to be discussed will include: Complex network topologies, methods for network analysis, visualization and simulation, models of dynamical/adaptive networks, techniques for mathematical analysis, network stability and robustness, and applications to social, biological and engineering systems. Python and NetworkX will be used for modeling and analysis of complex networks, in addition to other computational tools. Students should have a reasonable amount of experience in Python programming.

Schedule, slides & reading materials

- Week 1: Course introduction
- Network thinking: Some examples [slides]
- Fundamentals of graph theory [slides]
- Barabási, A. L. (2013). Network science. Phil. Trans. R. Soc. A, 371(1987), 20120375.
- Network Literacy: Essential Concepts and Core Ideas (2015). NetSciEd.
- Sayama, H., Cramer, C., Porter, M. A., Sheetz, L., & Uzzo, S. (2016). What are essential concepts about networks?. Journal of Complex Networks, 4(3), 457-474.

- Week 2: Classic graph theory problems [slides]
- Week 3: Topological analysis I: Statistical properties of networks [slides]
- Week 4: Random networks [slides]
- Week 5: Topological analysis II: Mesoscopic structures [slides]
- Week 6: Algebraic representation of networks [slides]
- Week 7: Simulation I: Dynamics of networks [slides]
- Week 8: Simulation II: Dynamics on networks [slides]
- Week 9: Simulation III: Adaptive networks [slides]
- Week 10: Recent topics I: Temporal networks [slides]
- Week 11: Recent topics II: Multilayer networks [slides]
- Week 12: Recent topics III: Higher-order interactions in networks [slides]
- Week 13: Final projects

- Week 14: Presentations

– Hiroki Sayama, Open SUNY Textbooks, 2015. http://bingweb.binghamton.edu/~sayama/textbook/*Introduction to the Modeling and Analysis of Complex Systems*

– Albert-László Barabási, Cambridge University Press, 2016. http://barabasi.com/book/network-science*Network Science*

– Albert-László Barabási, Basic Books, 2014.*Linked*

– Ernesto Estrada & Philip Knight, Oxford University Press, 2015.*A First Course in Network Theory*

– Alain Barrat, Marc Barthélemy & Alessandro Vespignani, eds., Cambridge University Press, 2008.*Dynamical Processes on Complex Networks*

– Thilo Gross & Hiroki Sayama, eds., Springer, 2009.*Adaptive Networks*

– David Easley & Jon Kleinberg, Cambridge University Press, 2010.*Networks, Crowds, and Markets*– Stefan Thurner, Rudolf Hanel, Peter Klimek, Oxford University Press, 2018.*Introduction to the Theory of Complex Systems*

*Questions? Comments? Email sayama@binghamton.edu*