XML and other types of semi-structured data are typically represented by a labeled directed graph. To speed up path expression queries over the graph, a variety of structural indexes have been proposed. They usually work by partitioning nodes in the data graph into equivalence classes and storing equivalence classes as index nodes. A(k)-index introduces the concept of local bisimilarity for partitioning, allowing the trade-off between index size and query answering power. However, all index nodes in A(k)-index have the same local similarity k, which cannot take advantage of the fact that a workload may contain path expressions of different lengths, or that different parts of the data graph may have different local similarity requirements. To overcome these limitations, we propose M(k)- and M*(k)-indexes. The basic M(k)-index is workload-aware: Like the previously proposed D(k)-index, it allows different index nodes to have different local similarity requirements, providing finer partitioning only for parts of the data graph targeted by longer path expressions. Unlike D(k)-index, M(k)-index is never over-refined for irrelevant index or data nodes. However, the workload-aware feature still incurs overrefinement due to over-qualified parent index nodes. Moreover, fine partitions penalize the performance of short path expressions. To solve these problems, we further propose the M*(k)-index. An M*(k)-index consists of a collection of indexes whose nodes are organized in a partition hierarchy, allowing successively coarser partitioning information to co-exist with the finest partitioning information required. Experiments show that our indexes are superior to previously proposed indexes in terms of index size and query performance.