Networks play an increasing role in society. Examples are the internet, social networks, phones networks and electricity and energy networks. Many of these structures have fascinating common properties. In this module we will have a look at the underlying mathematical theory that describes these structures. This theory, random graph theory, studies the collective behaviour of big sets of graphs and can be compared with the ordinary graph theory as statistical physics to the physics of Newton.

We will look at methods that will show that big networks have peculair properties. Furthermore, we study the time that is needed to let the network perform a certain task (like helping customers in a post office), look at strategies to search for information like Google does and look at how you can effectively spread information (or viruses) in networks. The underlying mathematics is that of random graphs and networks of queues.

A list of the different topics that will be covered:


Complex networks in practice: different manifestations, common structures. (Maurits de Graaf)


A first theoretical model, with far-reaching consequences (Maurits de Graaf)


Wait-and time calculation for logistic network processes (Nico van Dijk)


Two most simple network structures: complex? (Nico van Dijk)


Preferential attachment, or: how the rich are getting richer in complex networks. The impact of preferential attachment on robustness and spreading of information and viruses in networks. (Maurits de Graaf)


Why the world is 'small', search graphs and the basis of the Google PageRank algorithm (Maurits de Graaf)


Realisation of 'smart dust' networks: very small sensors in space: how we distribute energy and how we deal with problems involved with that (Maurits de Graaf)

General information

This course will take place in the third quartile of your second year. It will be given by Maurits de Graaf and Nico van Dijk.



Nico van Dijk

After a Ph.D. in Applied Mathematics and a visiting position at an American Business School, professor Nico van Dijk has been responsible for an Operations Research (OR) and Management (OM) Program at the University of Amsterdam for two decades. Since April 2012 he is affiliated to the University of Twente. He has a strong research interest in the area of stochastic OR, particularly Queueing. He also aims to popularize the potential of OR.  He has been involved in a variety of practical projects, among which for the Dutch railways, the Dutch airport Schiphol and KLM , the Dutch Triple A, the Dutch Ministry of Health and various hospitals, Dutch financial institutes (banks) and for over several years still is for the Dutch Bloodbank Sanquin



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Nelly Litvak

Nelly Litvak received her PhD from Eindhoven University of Technology (EURANDOM) in 2002. Last years she has been working on the analysis of complex networks, in particular, algorithms for node ranking, efficient detection of network structure, and analysis of network correlations. Her other research interests are in stochastic processes, queueing theory, and probabilistic solutions for combinatorial problems. Nelly has received several grants and awards including the Google Faculty Research Award 2012. She is a member of programme committees and invited speaker at many top conferences in mathematics and computer science and a managing editor of the Internet Mathematics journal.



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