The effective conductivities and the Dirichlet-to-Neumann operator of a network are invariant under the following star-mesh transform,

**Exercise (**)**. Use the Schur complement formula

for the Dirichlet-to-Neumann map to prove the invariance.

- The
*Y-Δ*transform is a special case of the star-mesh transform in which the center node has the degree*3*.