  A signed graph is a graph where the edges are assigned labels of either "$+$"
or "$-$". The sign of a cycle in the graph is the product of the signs of its
edges. We equip each signed complete graph with a vector whose entries are the
number of negative $k$-cycles for $k\in\{3,\dots,n\}$. These vectors generate
an affine subspace of $\mathbb{R}^{n-2}$. We prove that this subspace is all of
$\mathbb{R}^{n-2}$.
