In the context of stochastic search, once regions of high performance are found, having the property that small changes in the candidate solution correspond to searching nearby neighborhoods provides the ability to perform effective local optimization. To achieve this, Gray Codes are often employed for encoding ordinal points or discretized real numbers. In this paper, we present a method to label similar and/or close points within arbitrary graphs with small Hamming distances. The resultant point labels can be viewed as an approximate high-dimensional variant of Gray Codes. The labeling procedure is useful for any task in which the solution requires the search algorithm to select a small subset of items out of many. A large number of empirical results using these encodings with a combination of genetic algorithms and hill-climbing are presented.