  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.
