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Title: Mathematical modelling of evolving networks
Author: Parsons, Mark
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2013
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Network theory is a long standing, rapidly changing and highly motivated field. However, historically its results have been centred on static networks, leaving the area of evolving networks relatively less explored. In this thesis we draw from those existing results and extend them to the case of evolving networks to develop new analytical tools and representations. We do this through the introduction of an importance, or activity, metric for evolving networks, and the creation of a general framework for their models, allowing us to easily define, represent and classify them. We identify observable network properties and seek to predict the long term network structure of these modelled evolving networks. We find that networks can have a wide range of equilibria, even within the same model, from those devoid of network activity, to those exhibiting quasi-periodic network structure. These different equilibria within models are found to arise from chosen parameter values, highlighting the importance of their estimation. The properties upon which these models are based are often neglected for simplicity, however the application of our models to existing data proves their existence, and the significant variety of equilibria between network models shows us how important these properties are.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available