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Among other results, the purpose of this article is to show the existence ofan $\mathbb{R}$-space-vector with basis $\omega^i_j $, $i, j$ are integers suchthat every graph with n vertex $n \geq 3$ is the vector: $$\mathcal{V}(n) =\sum_{j=0}^{n-1} {\alpha^{n-1}_j} \omega^{n-1}_j $$ where $\alpha^{n-1}_j$ isthe number of sub graphs of type $\omega^{n-1}_j$ . We deduce that two graphsare isomorphic if for any measure, they have the same number of maximal propersubset with this measure.

Mesure et action des i-permutations sur les multigraphes multicolores finis et inifinis