  A signed graph is a graph whose edges are given (-1,+1) weights. In such a
graph, the sign of a cycle is the product of the signs of its edges. A signed
graph is called balanced if its adjacency matrix is similar to the adjacency
matrix of an unsigned graph via conjugation by a diagonal (-1,+1) matrix. For a
signed graph $\Sigma$ on n vertices, its exterior k-th power, where k=1,..,n-1,
is a graph $\bigwedge^{k} \Sigma$ whose adjacency matrix is given by \[
A({$\bigwedge^{k} {\Sigma}$}) = P^{\dagger} A(\Sigma^{\Box k}) P, \] where P is
the projector onto the anti-symmetric subspace of the k-fold tensor product
space $(\mathbb{C}^{n})^{\otimes k}$ and $\Sigma^{\Box k}$ is the k-fold
Cartesian product of $\Sigma$ with itself. The exterior power creates a signed
graph from any graph, even unsigned. We prove sufficient and necessary
conditions so that $\bigwedge^{k} \Sigma$ is balanced. For k=1,..,n-2, the
condition is that either $\Sigma$ is a signed path or $\Sigma$ is a signed
cycle that is balanced for odd k or is unbalanced for even k; for k=n-1, the
condition is that each even cycle in $\Sigma$ is positive and each odd cycle in
$\Sigma$ is negative.
