  We consider the rational flow $\xi_R(z)= R(z) (d/dz)$ where $R$ is given by
the quotient of two polynomials without common factors on the Riemann sphere.
The separatrix graph $\Gamma_R$ is the boundary between trajectories with
different properties. We characterize the properties of a planar directed graph
to be homeomorphic to the separatrix graph of a rational vector field on the
Riemann sphere.
