A realistic workload is essential in evaluating middleware for computational grids. One important component of that workload is the raw grid itself: an annotated graph representing the network topology and the hardware and software available on each node and link within it. GridG is an extensible synthetic generator of such graphs that is implemented as a series of transformations on a common graph format. The paper provides a definition of and requirements for grid generation. We then describe the GridG process in two steps: topology generation and annotation. For topology generation, we have both a model and a mechanism. We leverage Tiers, an existing tool commonly used in the networking community, but we extend it to produce graphs that conform to recently discovered power laws of Internet topology. We also contribute to the theory of network topology by pointing out a contradiction between two laws, and proposing a new version of one of them. For annotation, we have developed a mechanism, the requirements for a model, and identified the open problem of characterizing the distribution and correlation of hardware and software resources on the network.