Local bisimilarity has been proposed as an approximate structural summary for XML and other semi-structured databases. Approximate structural summary, such as A(k)-Index and D(k)-Index, reduce the index's size (and therefore reduce query evaluation time) by compromising on the long path queries. We introduce the A(k)-Simplified and the A(k)-Relevant, approximate structural summaries for graph documents in general, and for XML in particular. Like A(k)-Index and D(k)-Index, our indexes are based on local bisimilarity, however, unlike the previous indexes, they support the removal of non-relevant nodes. We also describe a way to eliminate false drops that might occur due to nodes removal. Our experiments shows that A(k)-Simplified and A(k)-Relevant are much smaller then A(k)-Index, and give accurate results with better performance, for short relevant path queries.