Graph Theoretic Approach Identifies Critical Thresholds at which Galaxy Filamentary Structures Form

Numerical simulations and observations show that galaxies are not uniformly distributed. In cosmology, the largest known structures in the universe are galaxy filaments formed from the hierarchical clustering of galaxies due to gravitational forces. These structures consist of walls and bridges that connect clusters. Here, we use graph theory to model the structures as Euclidean networks in three-dimensional space. Using percolation theory, cosmological graphs are reduced based on the valency of nodes to reveal the inner, most robust structural formation. By constraining the network, we then find thresholds for physical features, such as length-scale and density, at which galaxy filament clusters are identified.