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This paper presents a fast labeled graph matching algorithm called graph explorer (GE) algorithm, which can be categorized into the tree search based graph matching (TSGM) algorithms of exact graph/subgraph matching. Not like the other node-centric TSGM algorithms, the GE algorithm focuses on edges matching. It constructs search state of partially matched subgraph by edge and edge. It converts graph matching problem into a path search problem in the space of search states. Under the guidance of the search path, it avoided repeated label checking by inheriting state tree structure for caching and fast visiting matched nodes and edge. By a carefully optimized search route and intelligent backtracking, GE algorithm avoided a large amount of the invalid search states and improved performance to be almost linear to the number of edges of pattern graph with low ambiguity. While traditional TSGM are suffering the call stack overflow problem caused by recursive function calls, it overcame this problem by a dynamic state queue. It can handle extra large size of pattern (up to 10,000 nodes). The experiment shows the performance of GE is better than similar algorithms and it is more resistant to ambiguities.