In this paper, we revisit approaches for graph mining where a set of simple encodings is proposed. Complete approaches are those using an encoding allowing to get all the frequent subgraphs. Whereas incomplete approaches do not guarantee to nd all the frequent sub- graphs. Our objective is also to highlight the critical points in the process of extracting the frequent subgraphs with complete and incomplete ap- proaches. Current canonical encodings have a complexity which is of exponential nature, motivating this paper to propose a relaxation of canonicity of the encoding leading to complete and incomplete encod- ings with a linear complexity. These techniques are implemented within our graph miner GGM (Generic Graph Miner) and then evaluated on a set of graph databases, showing the behavior of both complete and incomplete approaches.