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

TL;DR

This paper applies graph theory and percolation analysis to cosmological data to identify critical thresholds for the formation of galaxy filaments, revealing structural properties of the universe.

Contribution

It introduces a novel graph-theoretic framework to determine physical thresholds for galaxy filament formation in cosmological structures.

Findings

Identifies length-scale and density thresholds for filament clusters

Models galaxy structures as Euclidean networks in 3D space

Reveals robust structural features through network reduction

Abstract

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.