Not sure what you mean... eig does return all of the eigenvectors and eigenvalues.
Do you mean that you need to know the degeneracy of the eigenvectors?
I think in general you have to do that numerically (and anyway approximately) by checking whether two eigenvalues are very close. If I recall correctly, the eigenvalues are output in ascending order (otherwise you can sort them).
Then, if E cointains your eigenvalues, you can check diff(E). If very small numbers appear, the corresponding eigenvectors are likely to be degenerate.
