  Cactus networks were introduced by Lam as a generalization of planar
electrical networks. He defined a map from these networks to the Grassmannian
Gr($n+1,2n$) and showed that the image of this map, $\mathcal X_n$ lies inside
the totally nonnegative part of this Grassmannian. In this paper, we show that
$\mathcal X_n$ is exactly the elements of Gr($n+1,2n$) that are both totally
nonnegative and isotropic for a particular skew-symmetric bilinear form. For
certain classes of cactus networks, we also explicitly describe how to turn
response matrices and effective resistance matrices into points of Gr($n+1,2n$)
given by Lam's map. Finally, we discuss how our work relates to earlier studies
of total positivity for Lagrangian Grassmannians.
