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The general linear group $GL_{n}$, along with its adjoint simple group$PGL_n$, can be described by means of weighted planar networks. In this paperwe give a network description for simple Lie groups of types $B$ and $C$. Thecorresponding networks are axially symmetric modulo a sequence of clustermutations along the axis of symmetry. We extend to this setting the result ofGekhtman, Shapiro, and Vainshtein on the Poisson property of Postnikov'sboundary measurement map. We also show that $B$ and $C$ type networks withpositive weights parametrize the totally nonnegative part of the respectivegroup. Finally, we construct network parametrizations of double Bruhat cells insymplectic and odd-dimensional orthogonal groups, and identify thecorresponding face weights with Fock-Goncharov cluster coordinates.

Planar networks and simple Lie groups beyond type A