  Twin vertices of a graph have the same open neighbourhood. If they are not
adjacent, then they are called duplicates and contribute the eigenvalue zero to
the adjacency matrix. Otherwise they are termed co-duplicates, when they
contribute $-1$ as an eigenvalue of the adjacency matrix. On removing a twin
vertex from a graph, the spectrum of the adjacency matrix does not only lose
the eigenvalue $0$ or $-1$. The perturbation sends a rippling effect to the
spectrum. The simple eigenvalues are displaced. We obtain a closed formula for
the characteristic polynomial of a graph with twin vertices in terms of two
polynomials associated with the perturbed graph. These are used to obtain
estimates of the displacements in the spectrum caused by the perturbation.
