The ?basis graph? approach to structural matching uses a fixed set of small (4 node) graphs to characterize local structure. We compute mapping probabilities by first finding the probability of a basis graph being an induced subgraph of the input graph. The similarity of these probabilities is used to compare nodes of the input graphs. The method permits common subgraphs to be identified without the use of any node or edge coloring. We report on an improved, simpler, version of the algorithm, which has also been optimized. Performance is compared with the LeRP method, which is based on length-r paths. Both methods are approximate with polynomial bounds on both memory and on the worst-case compute effort. These methods work on arbitrary types of undirected graphs, and tests with strongly regular graphs are included. Monte Carlo test trials (3000+) included up to 100% additional (noise) nodes.