Spectral characteristics of network redundancy.
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.
MacArthur
Ben D
BD
Department of Pharmacology and Systems Therapeutics, Systems Biology Center New York (SBCNY), Mount Sinai School of Medicine, New York, 10029 New York, USA. ben.macarthur@mssm.edu
Sánchez-García
Rubén J
RJ