The problem of discovering frequent subgraphs of graph data can be solved by constructing a candidate set of subgraphs first, and then, identifying within this candidate set those subgraphs that meet the frequent subgraph requirement. In Apriori-based graph mining, to determine candidate subgraphs from a huge number of generated adjacency matrices is usually the dominating factor for the overall graph mining performance since it requires to perform many graph isomorphism tests. To address this issue, we develop an effective algorithm for the candidate set generation. It is a hash-based algorithm and was confirmed effective through experiments on both real-world and synthetic graph data.