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On Diffusion Character Matrices

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dc.contributor.advisor Ashlock, Daniel Lee, Colin R. 2014-08-25T18:22:30Z 2014-08-25T18:22:30Z 2014-08 2014-08-14 2014-08-25
dc.description.abstract Graphs or networks are ubiquitous and useful mathematical objects, but comparing graphs can be computationally expensive and problematic for certain applications. This thesis introduces diffusion character matrices which are a way of transforming adjacency matrices of graphs in a useful manner for graph comparison. This thesis examines some mathematical theory behind diffusion character matrices, and investigates some of their applications. Diffusion character matrices are a useful way of generating graph invariants, and this thesis demonstrates that they can be used as a witness that graphs are non-isomorphic, can drastically reducing the number of permutations that need to be tested when computing the automorphism group of a graph, and can be used to construct useful pseudometrics on graphs. The primary application of diffusion character matrices examined in this thesis is the use of diffusion character based pseudometrics for distinguishing between different distributions of graphs. Several diffusion character based pseudometrics on graphs are used to provide statistical evidence that samples of graphs evolved to exhibit different epidemiological properties are drawn from different distributions of graphs. It is shown that for graph based epidemiological applications several diffusion character based pseudometrics are quite good at distinguishing between distributions of graphs. en_US
dc.description.sponsorship National Science and Engineering Research Council of Canada (NSERC),The University of Guelph. en_US
dc.language.iso en en_US
dc.rights Attribution-NonCommercial-ShareAlike 2.5 Canada *
dc.rights.uri *
dc.subject graph theory en_US
dc.subject pseudometrics en_US
dc.subject diffusion character matrices en_US
dc.subject pseudometric embedding en_US
dc.subject combinatorial graphs en_US
dc.subject evolutionary computation en_US
dc.title On Diffusion Character Matrices en_US
dc.type Thesis en_US Mathematics and Statistics en_US Doctor of Philosophy en_US Department of Mathematics and Statistics en_US
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