  In 2000, Dergachev and Kirillov introduced subalgebras of "seaweed type" in
$\mathfrak{gl}(n)$ and computed their index using certain graphs. In this
article, those graphs are called type-A meander graphs. Then the subalgebras of
seaweed type, or just "seaweeds", have been defined by Panyushev (2001) for
arbitrary simple Lie algebras. Namely, if $\mathfrak p_1,\mathfrak
p_2\subset\mathfrak g$ are parabolic subalgebras such that $\mathfrak
p_1+\mathfrak p_2=\mathfrak g$, then $\mathfrak q=\mathfrak p_1\cap\mathfrak
p_2$ is a seaweed in $\mathfrak g$. A general algebraic formula for the index
of seaweeds has been proposed by Tauvel and Yu (2004) and then proved by Joseph
(2006). If $\mathfrak p_1$ and $\mathfrak p_2$ are "adapted" to a fixed
triangular decomposition of $\mathfrak g$, then $\mathfrak q$ is said to be
standard. The number of standard seaweeds is finite.
  In this paper, elaborating on the "graphical" approach of Dergachev and
Kirillov, we introduce the type-C meander graphs, i.e., the graphs associated
with the standard seaweeds of $\mathfrak{sp}(2n)$, and give a formula for the
index in terms of these graphs. We also note that the very same graphs can be
used in case of the odd orthogonal Lie algebras. We also provide several
applications of our formula to the Frobenius seaweeds in $\mathfrak{sp}(2n)$.
In particular, using a natural partition of the set $\mathcal F_n$ of standard
Frobenius seaweeds, we prove that $\# \mathcal F_n$ strictly increases for the
passage from $n$ to $n+1$. The similar monotonicity question is open for the
standard Frobenius seaweeds in $\mathfrak{sl}(n)$, even for the passage from
$n$ to $n+2$.
