The modulation of promoter activity by DNA-binding transcription regulators forms a bipartite network between the regulators and genes, in which a smaller number of regulators control a much lager number of genes. To facilitate representation of gene expression data with the simplest possible network structure, we have characterized the ability of bipartite networks to describe data. This has led to the classification of two types of bipartite networks, versatile and nonversatile. Versatile networks can describe any data of the same rank, and are indistinguishable from one another. Nonversatile networks require constraints to be present in data they describe, which may be used to distinguish between different network topologies. By quantifying the ability of bipartite networks to represent data we were able to define connectivity efficiency, which is a measure of how economic the use of connections is within a network with respect to data representation and generation. We postulated that it may be desirable for an organism to maximize its gene expression range per network edge, since development of a regulatory connection may have some evolutionary cost. We found that the transcriptional regulatory networks of both Saccharomyces cerevisiae and Escherichia coli lie close to their respective connectivity efficiency maxima, suggesting that connectivity efficiency may have some evolutionary influence.