It is well known to associate an Euclidean graph to a molecule. Balasubramanian computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene [see Chem. Phys. Lett. 232 (1995), 415]. In this Letter, we proved an algorithm, which is useful for finding symmetry of molecules. Using this algorithm, a new simple method is described, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of the smallest fullerene C-20. Finally, an upper bound for the order of automorphism group of weighted graphs is obtained. (c) 2005 Elsevier B.V. All rights reserved.