  In this work we study a linear operator $f$ on a pre-euclidean space
$\mathcal{V}$ by using 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 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
$\B$.
