Biological data from high-throughput technologies describing the network components (genes, proteins, metabolites) and their associated interactions have driven the reconstruction and study of structural (topological) properties of large-scale biological networks. In this article, we address the relation of the functional and structural properties by using extensively experimentally validated genome-scale metabolic network models to compute observable functional states of a microorganism and compare the "structure versus function" attributes of metabolic networks. It is observed that, functionally speaking, the essentiality of reactions in a node is not correlated with node connectivity as structural analyses of other biological networks have suggested. These findings are illustrated with the analysis of the genome-scale biochemical networks of three species with distinct modes of metabolism. These results also suggest fundamental differences among different biological networks arising out of their representation and functional constraints.