### 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 [formula presented] depends on system size N as [formula presented] 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 [formula presented]

Original language | English |
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Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics