Prof. dr. Frank den Hollander, Mathematical Institute, Leiden University, The Netherlands : a course of lectures "Complex Networks: Structure and Functionality"

Dates & Location:June 19 – 21, 10:00-13:00,
Department of Mathematics, HSE, room 109.

Each part consists of 2 lectures and 1 exercise session, one hour each. Topics:

1. a. Examples of real-world networks, key questions, key challenges.
1. Random graphs, sequences of random graphs, key concepts: small world, scale free, hubs, clustering, communities, spatialness.
2. a.  Erd˝os-R´enyi Random Graph:  percolation on complete graphs.
1. Configuration Model: random graphs with prescribed degrees.
2. Phase transitions in the cluster sizes.
3. a. Google PageRank, WWW, size and volatility.
1. Random Walks on Dynamic Random Graphs: mixing times under random rewiring.

No prior knowledge of networks is required. Basic knowledge of probability theory and analysis are welcome.