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## Complex Networks

### Summary

EC | 8 |

Location | Vrije Universiteit |

Weeks | 6 - 21 |

Lecture | Tuesday, 14:00 - 16:45 |

Provider | Discrete Mathematics, Algebra and Number Theory (Diamant), Stochastics (Star) |

Links | Course page (requires login) |

**Prerequisites**

The course is aimed at master students in theoretical and applied mathematics and possibly physics and computer science. Solid knowledge of probability theory is necessary. Programming skills are optional. Students who like programming and applied problems can put it to use in a research assignment.

**Course description**

The Science of Complex Networks constitutes a young and active area of research, inspired by the empirical study of real-world networks (either physical, chemical, biological, economic or social). Most complex networks display non-trivial topological features, with patterns of connection that are neither purely regular nor purely random. Such features include a heavy tail in the empirical distribution of the number of edges incident to a vertex (scale freeness), insensitivity of this distribution to the size of the network (sparseness), small distances between most vertices (small world), likeliness that two neighbours of a vertex are also neighbours of each other (highly clustered), non-vanishing correlation between the numbers of edges incident to two neighbouring vertices (assortativity), community structure and hierarchical structure. The challenge is to understand the effect such features have on the performance of the network, via the study of models that allow for computation, prediction and control.

There will be 13 lectures in total: 1 introductory lecture by the four lecturers together, followed by 3 sets of 4 lectures by the four lecturers separately. For each lecture, a few students will be selected to read up on a particular network problem and provide a written report.

**Aim **

The aim of the course is to provide an introduction to the area, covering both theoretical principles and practical applications. The course has a kaleidoscopic character, approaching different topics from different viewpoints.

**Organization**

There will be 13 lectures in total: 1 introductory lecture by the four lecturers together, followed by 3 sets of 4 lectures by the four lecturers separately. For each lecture, a few students will be selected to read up on a particular network problem and provide a written report.

**Lecturers**

Frank den Hollander (LU), Michel Mandjes (UvA), Nelly Litvak (UT), Remco Hofstad (TU/e)

**Video recordings**

Video recordings can be found on https://vimeo.com/showcase/6865942

password: P18x