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Graphs are powerful data structures that have many attractive properties for object representation. However, some basic operations are difficult to define and implement, for instance, how to obtain a representative of a set of graphs. The median graph has been defined for that purpose, but existing algorithms are computationally complex and have a very limited applicability. In this paper we propose a new approach for the computation of the median graph based on graph embedding in vector spaces. Experiments on a real database containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results.