A Lie algebra L is Frobenius if there exists a functional L* such that the skew bilinear form (x,y) --> F([x,y]) is non-degenerate. The non-degeneracy of the form provides a natural isomorphism between L and L*, and thus there is a "Principal Element" of L corresponding to the linear functional F under this isomorphism. The spectrum of the principal element in the adjoint representation is independent of the choice of L and hence is an invariant of the algebra. In the case where L is a Frobenius subalgebra of sl(n) containing the Cartan subalgebra, the Ooms spectrum has particularly nice properties. All eigenvalues are integers which lie in the interval [1-n, n]. Moreover, they are "symmetric" around 1/2 in the sense that the dimension of the d-eigenspace equals that of the (1-d)-eigenspace). There is overwhelming evidence that the spectrum is a subinterval of [1-n,n], i.e. if p < q are eigenvalues then so is any other r with p < r < q. The assertion has been verified for thousands of examples. I will examine this question using graph theoretic techniques. Each non-degenerate functional produces a directed graph with no loops or isolated points. The eigenvalues of the principal element correspond to weighted path lengths in the graph. If the graph has certain desirable properties, then the spectrum is an interval. In all cases computed thus far, there exists a graph with such properties.