# Unit information: Complex Networks in 2021/22

Unit name Complex Networks MATH36201 20 H/6 Teaching Block 1 (weeks 1 - 12) Dr. Ayalvadi Ganesh Not open MATH11300 Probability 1 (or the first half of MATH10013 Probability and Statistics), MATH11005 Linear Algebra and Geometry and MATH20008 Probability 2 is strongly recommended. None School of Mathematics Faculty of Science

## Description including Unit Aims

Unit Aims

Networks are very widely used in mathematical modelling. They can describe physical systems such as transportation or telecommunication networks, or interactions between agents such as in social networks of humans or other biological organisms. It is of interest to study both the structure of the network, and dynamical processes occurring on a network.

Motivated by such questions, this unit will introduce a number of different random processes to model information spread, consensus formation, and random walks on networks. We will also study random network models and some of their properties.

The course will emphasise both proofs and applications.

Unit Description

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

• Probability background: Continuous time Markov chains and Poisson processes
• Spread of information and epidemics on networks
• Consensus formation on networks
• Random walks on networks and introduction to spectral graph theory
• Random graph models and properties

Relation to Other Units

The unit applies basic probabilistic models studied in Probability 2, specifically Markov chains and martingales, to the study of random processes on networks.

Graph theory would also have been introduced in Combinatorics. This unit does not have significant overlap with Combinatorics but takes a complementary approach to studying graphs using probability.

The course provides an interesting applied context for deepening the student's understanding of probabilistic techniques learnt in other courses such as Probability 2 and Martingale Theory and Applications.

## 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 Information

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

## Assessment Information

20% Coursework and 80% Examination.

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH36201).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.