  Many real-world complex networks contain a significant amount of structural
redundancy, in which multiple vertices play identical topological roles. Such
redundancy arises naturally from the simple growth processes which form and
shape many real-world systems. Since structurally redundant elements may be
permuted without altering network structure, redundancy may be formally
investigated by examining network automorphism (symmetry) groups. Here, we use
a group-theoretic approach to give a complete description of spectral
signatures of redundancy in undirected networks. In particular, we describe how
a network's automorphism group may be used to directly associate specific
eigenvalues and eigenvectors with specific network motifs.
