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Programme & Unit Catalogues

## MA30245: Graphs and networks: theory and applications

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must take XX10190 AND take MA10211 AND take MA10210
Description: Aims:
To introduce graph theory, from the mathematical fundamentals to modern applications in complex networks.

Learning Outcomes:
At the end of the course students should: understand basic graph theoretic definitions; be able to identify properties of graphs and networks; be familiar with the modelling and statistical characterisation of complex networks.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F

Content:
Fundamentals:
Graphs, digraphs, weighted graphs. Paths, spanning trees and connectedness. Matching and colouring. Max-flow min-cut. Degree distribution, clustering coefficient, clique number.
Graph algorithms. Modularity and community detection. Random network models, generation and simulation. Dynamics on networks, temporal networks.
Programme availability:

#### MA30245 is Optional on the following programmes:

Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• TSMA-AFM09 : MSc Mathematical Sciences
• TSMA-APM09 : MSc Mathematical Sciences
• TSMA-AFM08 : MSc Modern Applications of Mathematics
• TSMA-AWM14 : MSc Modern Applications of Mathematics
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.