Spectral Characteristics of Network Redundancy

Details Spectral Characteristics of Network Redundancy Spectral Characteristics of Network Redundancy

2009-04-21

arxiv.org/abs/0904.3192v2

Phys. Rev. E 80, 026117 (2009)

Physics

Physics and Society

12 pages, 51 figures, significant improvements

Scientific paper

10.1103/PhysRevE.80.026117

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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