Complex networks have recently become a vibrant branch of complexity science. Their ability to describe a variety of interacting systems, appearing in the natural and man-made environment, has led to its increased popularity in multiple scientific fields such as mathematics, physics, biology, computer science, sociology, epidemiology and many others. This thesis aims to further broaden the scope of complex networks by investigating physical models at a microscopic, mesoscopic and macroscopic scale. First we study the shapes of tree-like polymers comparing three different numerical and analytical methods (Wei, Benhamou and Monte Carlo methods). We find excellent agreement across all methods, indicating that increased branching generates more spherical objects. Secondly, UK Public transport networks are studied. Topological measures of robustness are investigated via the Molloy-reed parameter. Using fractal properties we extract information on the serviceability of stations and their efficiency. Thirdly, largescale structures of the universe are investigated. Here, we generate a network of the cosmic web to study its topological properties. Our main results indicate a correlation between clustering coefficient and the astrophysical properties of colour index and stellar mass.
|Date of Award||2018|