Journal
PHYSICAL REVIEW E
Volume 80, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.80.026117
Keywords
complex networks; eigenvalues and eigenfunctions; group theory; network theory (graphs); network topology
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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.
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