In recent years, large amount of data modeled by graphs, namely graph data, have been collected in various domains. Efficiently processing queries on graph databases has attracted a lot of research attentions. Supergraph query is a kind of new and important queries in practice. A supergraph query, q , on a graph database D is to retrieve all graphs in D such that q is a supergraph of them. Because the number of graphs in databases is large and subgraph isomorphism testing is NP-complete, efficiently processing such queries is a big challenge. This paper first proposes an optimal compact method for organizing graph databases. Common subgraphs of the graphs in a database are stored only once in the compact organization of the database, in order to reduce the overall cost of subgraph isomorphism testings from stored graphs to queries during query processing. Then, an exact algorithm and an approximate algorithm for generating significant feature set with optimal order are proposed to con...