A central problem in biology is determining how genes interact as parts of functional networks. Creation and analysis of synthetic networks, composed of well-characterized genetic elements, provide a framework for theoretical modeling. Here, with the use of a combinatorial method, a library of networks with varying connectivity was generated in Escherichia coli. These networks were composed of genes encoding the transcriptional regulators LacI, TetR, and lambda CI, as well as the corresponding promoters. They displayed phenotypic behaviors resembling binary logical circuits, with two chemical "inputs" and a fluorescent protein "output." Within this simple system, diverse computational functions arose through changes in network connectivity. Combinatorial synthesis provides an alternative approach for studying biological networks, as well as an efficient method for producing diverse phenotypes in vivo.