Probabilistic Foundations of Graphs and Networks – November 18

by Laurent Ménard (University Paris Ouest)

We will discuss some aspects of random graphs from a probabilistic point of view:

  • Different models of random graphs: Erdos-Renyi, configuration model, preferential attachment
  • Small world and scale free effects
  • Notions of convergence for large random graphs: dense versus diluted regime
  • Statistical models (contagion, percolation, …) on random graphs

Economics of Networks – November 19-20

by Sanjeev Goyal (University of Cambridge)

  • Introduction to network formation and introduction to games on networks
  • Recent developments: trading in networks, network resilience

Statistical Analysis of Network Data – November 19-20

by Eric Kolaczyk (Boston University)

Over the past decade, the study of so-called “complex networks” — that is, network-based representations of complex systems — has taken the sciences by storm. Researchers from biology to physics, from economics to mathematics, and from computer science to sociology, are more and more involved with the collection, modeling and analysis of network-indexed data. With this enthusiastic embrace of networks across the disciplines comes a multitude of statistical challenges of all sorts — many of them decidedly non-trivial. In this short course, we will cover a brief overview of the foundations common to the statistical analysis of network data across the disciplines, from a statistical perspective, in the context of topics like network summary and visualization, network sampling, network modeling and inference, and network processes. Concepts will be illustrated drawing on examples from bioinformatics, computer network traffic analysis, neuroscience, and social networks.

  • Introduction to the area
  • Network mapping (construction, visualization, etc.)
  • Network characterization
  • Network sampling
  • Network modeling