Graphs are widely used to model complicated data in many areas such as social networking, knowledge base, semantic web, bioinformatics and cheminformatics. More and more graph data are collected such that it has become a rather challenging problem to manage such complex data. The database community has had a long-standing interest in querying graph databases, and graph similarity search is one of most popular topics. This paper focuses on the graph similarity search problem with edit distance constraints. Firstly, several state-of-the-art methods are investigated to reveal that all the proposed pruning rules have limitations and none of them can outperform others on various queries. To address this problem, then a novel approach is proposed to support the graph similarity search in the framework of query evaluation using the relational model. The proposed approach develops a novel unified filtering framework by combing all the existing pruning rules. It can avoid limitations on existing pruning rules, and have more widely applications. A series of experiments are also conducted to evaluate the proposed approach. The results show that the new approach can outperform all existing state-of-the-art methods.