IC17 – Small-World Networks: What Facebook and Roundworm Brains Have in Common

Lecturer: Emily J King
Fields: graph theory


A network or graph is a way to model objects or organisms and their connections with each other. One example of a network is to connect Facebook users if they are friends on the website. Although the number of Facebook accounts is on the order of 1 billion and the average number of Facebook friends each user has is approximately 100, on average any two users are connected by a chain of less than 4 intermediary Facebook friends. Such a network – where the average number of connections per object is “low” but the average distance between objects is also “low” is called a small-world network. Small-world networks appear in many applications and can influence the spread of disease. In this short talk, we will learn a bit about small-world networks and some examples where they appear.


  • “Collective dynamics of ‘small-world’ networks”, Duncan J. Watts & Steven H. Strogatz, Nature volume 393, pages440–442 (1998), https://www.nature.com/articles/30918
  • “Four Degrees of Separation”, Lars Backstrom, Paolo Boldi, et. al, WebSci ’12: Proceedings of the 4th Annual ACM Web Science Conference, pages 33–42 (June 2012), https://dl.acm.org/doi/10.1145/2380718.2380723


Emily J King
Prof. Emily King

Prof. King (Emily) studies how to best deconstruct things into fundamental building blocks in order to better understand them. This can range from tearing apart neural networks to try to figure out how they work to developing methods for extracting features out of biomedical images to finding building blocks with beautiful mathematical symmetries that are also useful in quantum information. She is abusing the special nature of the 2021 Virtual IK to both give a talk and serve as co-chair, which is usually a big no-no. =-.) Prof. King is currently a professor in the Mathematics Department at Colorado State University. Before, she was a professor at the University of Bremen; a Humboldt Fellow at the Technical University of Berlin, the University of Bonn, and the University of Osnabrück; a IRTA Postdoc Fellow at the National Institutes of Health; and a Ph.D. student at the University of Maryland. Please feel free to chat with her if you see her around virtual Günne. Photo credit: MFO / Petra Lein

Affiliation: Colorado State University
Homepage: https://www.math.colostate.edu/~king/