Faculty of Science AMSI Summer School 2013

Complex networks

Stephen Davis (RMIT)


Synopsis

The world around us is brimming with structure that consists of discrete entities and relationship between those entities. These structures can be represented as a set of vertices and a set of links that formally define a graph, and a complex network is nothing more than a very large graph where the links are neither predictable nor completely random. This course will touch on the analysis of real, complex networks that arise in ecology and epidemiology, such as food webs and wildlife contact networks, but will emphasise the mathematical and statistical techniques used to classify and characterise networks. The course will begin with a focused study of graph theory as the mathematical basis for network science.

Course content:


Contact hours

28 hours of lectures and in-class exercises spread over 4 weeks.


Prerequisites

Students will be asked to implement algorithms and analyse real network data, and hence should be confident and comfortable with at least one programming language. The course includes examples where algorithms are implemented in the environment R (http://www.r-project.org/) and this is the preferred option for students for carrying out assignment work, even if they have not encountered R before attending the summer school.


Assessment

Two assignments, each worth 20%, and a take home exam worth 60%.


Resources

Lecture notes I and II are now available for download. These same resources will be provided in hardcopy.

There is an excellent and recent textbook on networks by the prolific physicist and network scientist M.E.J. Newman: Networks: An introduction, Oxford University Press, 2010.

The statistical programming environment known as R (http://www.r-project.org/) is freely available for download. The course, and particularly the assessment tasks, includes implementing algorithms and applying them to real data sets. If students do have a laptop, then they should make sure to bring it with them and to download and install the free R software.


About Stephen Davis

Stephen was born in Victoria, Australia, and studied mathematics as an undergraduate at the University of Melbourne. He went on to do a PhD in Applied Mathematics (University of New South Wales) before leaving Australia in 2001 to take up a guest professorship at the University of Antwerp in Belgium. Some 8 years later, with stints at the University of Utrecht in The Netherlands and at Yale University in the United States, he returned to Australia and to Melbourne and is currently a Senior Lecturer at RMIT University. Stephen’s principal research theme is real-world application of discrete structures which encompasses diverse areas such as mathematical epidemiology, theoretical population ecology and pattern matching in biometric identification.

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