Geometric graphs, the cosmic web and hypergraphs

• Online Access: http://hdl.handle.net/2047/D20214150

First, we show how network science can be applied to study the cosmic web and we explore a hypothetical spreading process at the cosmic level using concepts from network science. The concept of the cosmic web, viewing the Universe as a set of discrete galaxies held together by gravity, is deeply engrained in cosmology. Yet, little is known about the most effective construction and the characteristics of the underlying network. We explore seven network construction algorithms that use various galaxy properties, from their location to their size and relative velocity. We find that a model relying only on spatial proximity offers the best correlations between the physical characteristics of the connected galaxies. We show that the properties of the networks generated from simulations and observations are identical, unveiling a deep universality of the cosmic web. Second, we explore a generalization of graphs, called hypergraphs, which offer a much more faithful representation of many complex systems. We find that in most real-world hypergraphs two key combinatorial problems, the edge and the vertex cover problems, can be solved in polynomial time.