### Abstract

Language | English |
---|---|

Pages | 3648-3660 |

Number of pages | 12 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 389 |

Issue number | 17 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- Network vibrations
- Centrality
- Spectral theory
- Kirchhoff index
- Information centrality
- Social networks

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*389*(17), 3648-3660. https://doi.org/10.1016/j.physa.2010.03.030

}

*Physica A: Statistical Mechanics and its Applications*, vol. 389, no. 17, pp. 3648-3660. https://doi.org/10.1016/j.physa.2010.03.030

**A vibrational approach to node centrality and vulnerability in complex networks.** / Estrada, Ernesto; Hatano, N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A vibrational approach to node centrality and vulnerability in complex networks

AU - Estrada, Ernesto

AU - Hatano, N.

PY - 2010

Y1 - 2010

N2 - We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

AB - We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

KW - Network vibrations

KW - Centrality

KW - Spectral theory

KW - Kirchhoff index

KW - Information centrality

KW - Social networks

U2 - 10.1016/j.physa.2010.03.030

DO - 10.1016/j.physa.2010.03.030

M3 - Article

VL - 389

SP - 3648

EP - 3660

JO - Physica A: Statistical Mechanics and its Applications

T2 - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 17

ER -