  It is well-known that the space of derivations of $n$-dimensional evolution
algebras with non-singular matrices is zero. On the other hand, the space of
derivations of evolution algebras with matrices of rank $n-1$ has also been
completely described in the literature. In this work we provide a complete
description of the space of derivations of evolution algebras associated to
graphs, depending on the twin partition of the graph. For graphs without twin
classes with at least three elements we prove that the space of derivations of
the associated evolution algebra is zero. Moreover, we describe the spaces of
derivations for evolution algebras associated to the remaining families of
finite graphs. It is worth pointing out that our analysis includes examples of
finite dimensional evolution algebras with matrices of any rank.
