In order to enable scalable querying of graph databases, intelligent selection of subgraphs to index is essential. An improved index can reduce response times for graph queries significantly. For a given subgraph query, graph candidates that may contain the subgraph are retrieved using the graph index and subgraph isomorphism tests are performed to prune out unsatisfied graphs. However, since the space of all possible subgraphs of the whole set of graphs is prohibitively large, feature selection is required to identify a good subset of subgraph features for indexing. Thus, one of the key issues is: given the set of all possible subgraphs of the graph set, which subset of features is the optimal such that the algorithm retrieves the smallest set of candidate graphs and reduces the number of subgraph isomorphism tests? We introduce a graph search method for subgraph queries based on subgraph frequencies. Then, we propose several novel feature selection criteria, Max-Precision, Max-Irredundant-Information, and Max-Information-Min-Redundancy, based on mutual information. Finally we show theoretically and empirically that our proposed methods retrieve a smaller candidate set than previous methods. For example, using the same number of features, our method improve the precision for the query candidate set by 4%-13% in comparison to previous methods. As a result the response time of subgraph queries also is improved correspondingly.