  Amalgamation in the totally non-negative part of positroid varieties is
equivalent to gluing copies of $Gr^{TP}(1,3)$ and $Gr^{TP}(2,3)$. Lam has
proposed to represent amalgamation in positroid varieties by equivalence
classes of relations on bipartite graphs and identify total non-negativity via
edge signatures. Here we provide an explicit characterization of such
signatures on the planar bicolored trivalent directed perfect networks in the
disk parametrizing positroid cells $S_M^{TNN}$.To a graph $G$ representing
$S_M^{TNN}$, we associate a geometric signature satisfying full rank condition
and total non--negativity. Such signature is uniquely identified by geometric
indices ruled by orientation and gauge ray direction. The image of this map
coincides with that of Postnikov boundary measurement map. We solve the system
of geometric relations generalizing Postnikov's and Talaska's results for the
boundary edges to the internal edges of the graphs: the edge vector components
are rational in the weights with subtraction--free denominators, and have
explicit expressions in terms of conservative and edge flows. At boundary
sources the edge vectors give the boundary measurement matrix. If $G$ is
acyclically orientable, all components are subtraction-free rational in the
weights w.r.t. a convenient basis. We provide explicit formulas for the
transformation rules w.r.t. changes the orientation, the several gauges of the
given network, moves and reductions of networks. We show that the image of the
boundary measurement map and the dimer partition functions do not coincide if
the graph is not bipartite.
