Spectra and eigenvectors of scale-free networks

by: KI Goh, B Kahng, D Kim

Physical Review E, Vol. 64, No. 5. (15 October 2001), 051903.

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Abstract

We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bidirectional interaction is allowed; so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center; followed by power-law long tails at both spectrum edges. The largest eigenvalue λ 1 depends on system size N as λ 1 ∼ N 1/4 for large N ; and the corresponding eigenfunction is strongly localized at the hub; the vertex with largest degree. The component of the normalized eigenfunction at the hub is of order unity. We also find that the mass gap scales as N -0.68 .

@article{citeulike:1353026, abstract = {We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bidirectional interaction is allowed; so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center; followed by power-law long tails at both spectrum edges. The largest eigenvalue λ 1 depends on system size N as λ 1 ∼ N 1/4 for large N ; and the corresponding eigenfunction is strongly localized at the hub; the vertex with largest degree. The component of the normalized eigenfunction at the hub is of order unity. We also find that the mass gap scales as N -0.68 .}, author = {Goh, K. I. and Kahng, B. and Kim, D. }, citeulike-article-id = {1353026}, doi = {10.1103/PhysRevE.64.051903}, journal = {Physical Review E}, keywords = {eigenvectors, networks, scalefree, spectra}, month = {October}, number = {5}, pages = {051903+}, posted-at = {2007-05-31 23:41:06}, priority = {2}, publisher = {American Physical Society}, title = {Spectra and eigenvectors of scale-free networks}, url = {http://dx.doi.org/10.1103/PhysRevE.64.051903}, volume = {64}, year = {2001} }

RIS record

TY - JOUR ID - citeulike:1353026 L3 - citeulike-article-id:1353026 TI - Spectra and eigenvectors of scale-free networks JF - Physical Review E VL - 64 IS - 5 SP - 051903 PB - American Physical Society N2 - We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bidirectional interaction is allowed; so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center; followed by power-law long tails at both spectrum edges. The largest eigenvalue λ 1 depends on system size N as λ 1 ∼ N 1/4 for large N ; and the corresponding eigenfunction is strongly localized at the hub; the vertex with largest degree. The component of the normalized eigenfunction at the hub is of order unity. We also find that the mass gap scales as N -0.68 . KW - eigenvectors KW - networks KW - scalefree KW - spectra AU - Goh, KI AU - Kahng, B AU - Kim, D PY - 2001/10/15/ UR - http://dx.doi.org/10.1103/PhysRevE.64.051903 ER -

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