Text cohesion is an important element of discourse processing. This paper presents a new approach to modeling, quantifying, and visualizing text cohesion using automated cohesion flow indices that capture semantic links among paragraphs. Cohesion flow is calculated by applying Cohesion Network Analysis, a combination of semantic distances, Latent Semantic Analysis, and Latent Dirichlet Allocation, as well as Social Network Analysis. Experiments performed on 315 timed essays indicated that cohesion flow indices are significantly correlated with human ratings of text coherence and essay quality. Visualizations of the global cohesion indices are also included to support a more facile understanding of how cohesion flow impacts coherence in terms of semantic dependencies between paragraphs.