Title: Graph Theoretic Approach to Investigationg the 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 consist of "walls" and "bridges" that connect clusters. Using the Julia programming language, this study takes a graph theoretic approach to model these structures as euclidean networks in three dimensional space. Continuing with a method borrowed from statistical physics and 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 are able to identify a threshold for physical features such as length-scale and density, at which galaxy filaments in clusters can be identified.