  One can realize higher laminations as positive configurations of points in
the affine building. The duality pairings of Fock and Goncharov give pairings
between higher laminations for two Langlands dual groups $G$ and $G^{\vee}$.
These pairings are a generalization of the intersection pairing between
measured laminations on a topological surface.
  We give a geometric interpretation of these intersection pairings in the case
that $G=SL_n$. In particular, we show that they can be computed as the length
of minimal weighted networks in the building. Thus we relate the intersection
pairings to the metric structure of the affine building. This proves several of
the conjectures from [LO]
  The key tools are linearized versions of well-known classical results from
combinatorics, like Hall's marriage lemma, Konig's theorem, and the
Kuhn-Munkres algorithm.
