he reverse engineering of biological networks is an important and interesting problem. Two examples of such networks are gene regulatory networks, and the relationship of voxels in the brain. We describe a method for determining possible "wiring diagrams" for such networks. The method is based on computational algebra, and a key part of the method uses computations involving monomial ideals in a polynomial ring. To illustrate the algorithms, we apply the method to data coming from fMRI scans of the brain. This talk represents joint work (on the arXiv at q-bio.QM/0605032) with Abdul Jarrah, Reinhard Laubenbacher, and Brandy Stigler. The analysis of the brain data was performed by Paola Vera.