Dynamic hyperbolic graphs – GrHyDy

In complex networks, it has been empirically observed that many networks typically are scale-free and exhibit a non-vanishing clustering coefficient. Models of complex networks that naturally exhibits these properties are random graph models in the hyperbolic plane, such as the random hyperbolic graph model by Krioukov et al. and other variants. In this project we aim to analyze rigorously parameters related to the flow/exchange of information in random hyperbolic graphs, arguably one of the most important parameters of complex networks. Our goal is to contribute to establish the foundation for these random graph models; in particular we aim at analyzing percolation together with component sizes, broadcasting times of rumors, hitting times of random walks, and extinction times of the contact process. Our second objective is also to set up a dynamic graph model and to analyze the aforementioned parameters in the dynamic setup.