  We provide in this paper a sufficient condition for a polynomial dynamical
system $\dot x(t) = f(x(t))$ to be super-linearizable, i.e., to be such that
all its trajectories are linear projections of the trajectories of a linear
dynamical system. The condition is expressed in terms of the hereby introduced
weighted dependency graph $G$, whose nodes $v_i$ correspond to variables $x_i$
and edges $v_iv_j$ have weights $\frac{\partial f_j}{\partial x_i}$. We show
that if the product of the edge weights along any cycle in $G$ is a constant,
then the system is super-linearizable. The proof is constructive, and we
provide an algorithm to obtain super-linearizations and illustrate it on an
example.
