Inhomogeneous spatial networks - beyond the weak decay regime
Description Phase 2
Complex Networks arise throughout the sciences wherever large systems of interacting objects are investigated. In this project we study a rich class of mathematical network models that satsify three basic principles: scale-freeness, the small-world property and clustering. To generate the models we form graphs consisting of randomly distributed vertices equipped with a weight, which are then connected by edges. The generation of each edge takes into account both the spatial distance between its endvertices as well as their weight. Our goal is to understand the behaviour of these models by answering questions such as: When are there large connected components? What are their topological properties, e.g. connectivity and interpoint graph distances? Do they qualitatively behave more like lattices or more like trees? And what happens if we randomly remove edges from them?