Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.629965
Title: Structure and dynamics of evolving complex networks
Author: Colman, Ewan
ISNI:       0000 0004 5351 3168
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 2014
Availability of Full Text:
Access through EThOS:
Access through Institution:
Abstract:
The analysis of large disordered complex networks has recently received enormous attention motivated by both academic and commercial interest. The most important results in this discipline have come from the analysis of stochastic models which mimic the growth and evolution of real networks as they change over time. The purpose of this thesis is to introduce various novel processes which dictate the development of a network on a small scale, and use techniques learned from statistical physics to derive the dynamical and structural properties of the network on the macroscopic scale. We introduce each model as a set of mechanisms determining how a network changes over a small period in time, from these rules we derive several topological properties of the network after many iterations, most notably the degree distribution. 1. In the rst mechanism, nodes are introduced and linked to older nodes in the network in such a way as to create triangles and maintain a high level of clustering. The mechanism resembles the growth of a citation network and we demonstrate analytically that the mechanism introduced su ces to explain the power-law form commonly found in citation distributions. 2. The second mechanism involves edge rewiring processes - detaching one end of an edge and reattaching it, either to a random node anywhere in the network or to one selected locally. 3. We analyse a variety of processes based around a novel fragmentation mechanism. 4. The nal model concerns the problem of nding the electrical resistance across a network. The network grows as a random tree, as it grows the distribution of resistance converges towards a steady state solution. We nd an application of the relatively recent concept of a random Fibonacci sequence in deriving the rate of convergence of the mean.
Supervisor: Rodgers, G. Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.629965  DOI: Not available
Keywords: Statistical mechanics ; Complex systems ; Physics ; Mathematical modelling ; Mathematics
Share: