Graph-structured databases and related problems such as reachability query processing have been increasingly relevant to many applications such as XML databases, biological databases, social network analysis and the Semantic Web. To efficiently evaluate reachability queries on large graph-structured databases, there has been a host of recent research on graph indexing. To date, reachability indexes are generally applied to the entire graph. This can often be suboptimal if the graph is large or/and its subgraphs are diverse in structure. In this paper, we propose a uniform framework to support existing reachability indexingfor subgraphs of a given graph. This in turn supports fast reachability query processing in large graph-structured databases. The contributions of our uniform framework are as follows: (1) We formally define a graph framework that facilitates indexing subgraphs, as opposed to the entire graph. (2) We propose a heuristic algorithm to partition a given graph into subgraphs for indexing.(3) We demonstrate how reachability queries are evaluated in the graph framework. Our preliminary experimental results showed that the framework yields a smaller total index size and is more efficient in processing reachability queries on large graphs than a fixed index scheme on the entire graphs.