In this work, we study a linear operator \( f \) on a pre-euclidean space \( \mathcal V \) by using the properties of a corresponding graph. Given a basis \( B \) of \( \mathcal V \), we present a decomposition of \( \mathcal V \) as an orthogonal direct sum of certain linear subspaces \( \{U_i\}_{i\in I} \) each one admitting a basis inherited from \( B \), in such way that \( f=\sum_{i\in I}f_i \) being each \( f_i \) a linear operator satisfying certain conditions respect with \( U_i \). Considering a new hypothesis, we assure the existence of an isomorphism between the graphs associated to \( f \) relative to two different bases. We also study the minimality of \( \mathcal V \) by using the graph associated to \( f \) relative to \( B \).