  A collection $\mathcal{C}$ of $k$-element subsets of $\{1,2,\ldots,m\}$ is
weakly separated if for each $I, J \in \mathcal{C}$, when the integers
$1,2,\ldots,m$ are arranged around in a circle, there is a chord separating $I
\backslash J$ from $J \backslash I$. Oh, Postnikov and Speyer constructed a
correspondence between weakly separated collections which are maximal by
inclusion and reduced plabic graphs, a class of networks defined by Postnikov
which give coordinate charts on the Grassmannian of $k$-planes in m-space. As a
corollary, they proved Scott's Purity Conjecture, which states that a weakly
separated collection is maximal by inclusion if and only if it is maximal by
size. In this note, we describe maximal weakly separated collections
corresponding to symmetric plabic graphs, which give coordinate charts on the
Lagrangian Grassmannian, and prove a symmetric version of the Purity
Conjecture.
