  Following de Verdi\`{e}re-Gitler-Vertigan and Curtis-Ingerman-Morrow, we
prove a host of new results on circular planar electrical networks. We
introduce a poset EP_{n} of electrical networks with n boundary vertices,
giving two equivalent characterizations, one combinatorial and the other
topological. We then investigate various properties of the EP_{n}, proving that
it is graded by number of edges of critical representatives. Finally, we answer
various enumerative questions related to EP_{n}, adapting methods of Callan and
Stein-Everett.

Combinatorics