MSc Math Defence: A Novel Representation for Graph Evolution

Meghan Timmins, M.Sc. Thesis Defence

Networks and combinatorial graphs are commonly used in a wide variety of types of mathematical modelling to represent structures such as contact networks in epidemiology, road networks in urban planning, and scheduling conflicts.

Introduction to the topic of graphs comes through a brief look at the community assembly problem. A new method for community using evolutionary computation is established and compared to a pre-existing method. We then examine the novel problem of graph evolution and develop a new graph representation, one that expands previously effective representations. The expansion includes the addition of two new operators to yield the THADSN representation which allows for both local and global adjustment of connectivity. We examine three benchmark functions on which to test the THADSN representation. The test problems are used to compare the new representation with the previously used TADS representation.

A copy of the thesis is available (pdf format) from Susan McCormick for examination and comment.