# Unit information: Complex Networks in 2015/16

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Unit name Complex Networks MATH36201 20 H/6 Teaching Block 1 (weeks 1 - 12) Dr. Ayalvadi Ganesh Not open MATH11300 Probability 1 (or equivalent) and MATH 11005 Linear Algebra & Geometry (or equivalent). MATH 21400 (Applied Probability 2) is strongly recommended. none School of Mathematics Faculty of Science

## Description

Unit aims

Understand how to mathematically model complex networks. Learn to analyse stochastic processes such as rumour spread, epidemics and consensus on networks.

General Description of the Unit

This unit will teach ways of modelling and working with large complex networks such as the Internet and social networks. The topics covered will be

Probability background: Markov chains in discrete and continuous time, and Poisson processes Spread of information and epidemics on networks Consensus models on networks Random walks on networks and spectral graph theory Random graphs

Relation to Other Units

The unit introduces Markov chain models seen in Applied Probability 2 (which is not a pre-requisite but is strongly recommended) and applies them to the study of random processes on networks. Information Theory, Complex Networks, Financial Mathematics, and Queueing Networks, all involve the application of probability theory to problems arising in various fields.

Applied Probability 2 will become a pre-requisite for this course from next year. Students who have not taken it should discuss the suitability of this course with the unit organiser before registering for it.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended learning outcomes

Learning Objectives

• Learn to model a variety of stochastic processes on graphs, including random walks and the spread of information and epidemics
• Learn to analyse these processes to obtain bounds and approximations for quantities of interest
• Learn about the relationship of graph spectra to various properties of the graph

## Teaching details

Lectures and problem sheets, from which work will be set and marked, with outline solutions handed out a fortnight later.

## Assessment Details

100% Examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.