Algorithms for Complex Networks + Applied Probability and Stochastic Operations Research
University of Twente and Eindhoven University of Technology
Nelly Litvak is a professor at the University of Twente and Eindhoven University of Technology in the Netherlands. She received the Stieltjes prize for the best PhD thesis and the Google faculty research award. She is a managing editor of Internet Mathematics and an associate editor of Stochastic Processes and their Applications. She is a finalist of the 2017 Enlightener award for the best popular science book in Russia. Her research interests are in the study of large networks such as on-line social networks and the World Wide Web, randomized algorithms, and random graphs.
Networks as random graphs
Suppose that a data is available of a large real-life network, for example a web crawl or a Twitter discussion. It is now a common practice in Networks Science to compute network statistics, such as degree distributions, and look for patterns by comparing the data to a `null-model’. During this talk, I will discuss this approach from the mathematical view point. We start with degree distributions: what does it mean that the distribution is `scale-free’ and what effect it has on the network’s statistics. Next, we will address several most common `null-models’ in the theory of random graphs. We will discuss comparative advantages and caveats of these models, and the assumptions behind them. At the end, we will shortly address the difficult problem of fitting models to data.