With the ability to observe the atmospheres of terrestrial exoplanets via transit spectroscopy on the near-term horizon, the possibility of atmospheric biosignatures has received considerable attention in astrobiology. While traditionally exoplanet scientists looking for life focused on biologically relevant trace gases such as O2 and CH4, this approach has raised the spectre of false positives. Therefore, to address these shortcomings, a new set of methods is required to provide higher confidence in life detection. One possible approach is measuring the topology of atmospheric chemical reaction networks (CRNs). To investigate and assess this approach, the ability of network-theoretic metrics to distinguish the distance from thermochemical equilibrium in the atmosphere of hot jupiters was tested. After modeling the atmospheres of hot jupiters over a range of initial conditions using the VULCAN modeling package, atmospheric CRNs were constructed from the converged models and their topology measured using the Python package NetworkX. I found that network metrics were able to predict the distance from thermochemical equilibrium better than atmospheric species abundances alone. Building on this success, I modeled 30,000 terrestrial worlds. These models divided into two categories: Anoxic Archean Earth-like planets that varied in terms of CH4 surface flux (modeled as either biotic or abiotic in origin), and modern Earth-like planets with and without a surface flux of CCl2F2 (to represent the presence of industrial civilizations). I constructed atmospheric CRNs from the converged models, and analyzed their topology. I found that network metrics could distinguish between atmospheres with and without the presence of life or technology. In particular, mean degree and average shortest path length consistently performed better at distinguishing between abiotic and biotic Archean-like atmospheres than CH4 abundance.