The EC of graphs and manifolds provides a topological descriptor that summarizes and quantifies complex structures and patterns that arise in MD simulations. The EC can be used to conduct a wide variety of ML and data analysis tasks such as visualization, clustering, regression, and classification. Here, we demonstrate that the EC of a molecular system correlates strongly to emergent physical and chemical characteristics. As such, we show that the EC can be used as an informative descriptor to predict emergent behavior; moreover, we show that such predictions can be conducted using simple linear regression models (easier to build and analyze), which contrasts with existing approaches based on CNNs.