Correlation networks are emerging as powerful tools for modeling relationships in high-throughput data such as gene expression. Other types of biological networks, such as protein-protein interaction networks, are popular targets of study in network theory, and previous analysis has revealed that network structures identified using graph theoretic techniques often relate to certain biological functions. Structures such as highly connected nodes and groups of nodes have been found to correspond to essential genes and protein complexes, respectively. The correlation network, which measures the level of co-variation of gene expression levels, shares some structural properties with other types of biological networks. We created several correlation networks using publicly available gene expression data, and identified critical groups of nodes using graph theoretic properties used previously in other biological network studies. We found that some measures of network centrality can reveal genes of impact such as essential genes, suggesting that the correlation network can prove to be a powerful tool for modeling gene expression data. In addition, our method highlights the biological impact of nodes a set of high centrality nodes identified by combined measures of centrality to validate the link between structure and function in the notoriously noisy correlation network.