Module Code
TGI_M02
Module Title
Modelling and Searching Networks
Host Institution/
Contact
NUI Maynooth, Robert Shorten
Pre-requisites
An undergraduate course in graph theory or discrete mathematics.
An undergraduate course in linear algebra and one in elementary
probability are recommended.
ECTS
5
Anthony Bonato,
Ryerson University, Canada
Chief Examiner
Teaching Staff
Delivery
24 hours of lectures over a two week period.
April/May 2013
Aims
To provide an introduction to two central topics in the contemporary
theory of networks and graph theory: complex networks and vertex
pursuit games. Students taking the course will receive a broad
introduction to the state-of-the-art tools, results, and open problems
in both areas.
The first week will focus on the modelling of complex, real-world
networks such as the web graph, on-line social networks, and
protein interaction networks. After a discussion of the properties of
complex networks, we will introduce random graph models such as
preferential attachments, copying, and various geometric models.
Google’s PageRank web search algorithm will also be discussed.
In the second half, the course will focus on vertex pursuit games
such as Cops and Robbers. Topics will include the structure of copwin graphs, Meyniel’s conjecture, the cop number in graph classes,
the cop number of random graphs, and variants of the game such
as Firefighter.
Target audience: Graduate or advanced undergraduate students in
Mathematics, Computer Science, and Engineering.
Syllabus
1) Review of graph theory.
2) Complex networks: properties and function.
3) Random graphs.
4) Random graph models for complex networks.
5) On-line social networks and geometric graphs.
6) An introduction to web search and PageRank.
7) Introduction to vertex pursuit games.
8) Cops and Robbers games and cop number.
9) Cop-win graphs.
10) Meyniel’s conjecture.
11) Cop number of planar graphs.
12) Cop number of random graphs.
13) Variants of Cops and Robber games.
14) Firefighting and Seepage.
Assessment
Assessment: one 2-hour examination
Bibliography
A. Bonato, A Course on the Web Graph, Graduate Studies in
Mathematics Series, American Mathematical Society, Providence,
Rhode Island, 2008.
A. Bonato and R.J. Nowakowski, The Game of Cops and Robbers
on Graphs, American Mathematical Society, Providence, Rhode
Island, 2011.