### Abstract

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

Pages | 764-774 |

Number of pages | 10 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 388 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 Mar 2009 |

### Fingerprint

### Keywords

- centrality measures
- proteinprotein interactions
- communicability
- spectral graph theory
- conserved proteins
- linear response
- fréchet derivative

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*388*(5), 764-774. https://doi.org/10.1016/j.physa.2008.11.011

}

*Physica A: Statistical Mechanics and its Applications*, vol. 388, no. 5, pp. 764-774. https://doi.org/10.1016/j.physa.2008.11.011

**Communicability betweenness in complex networks.** / Estrada, Ernesto; Higham, Desmond J.; Hatano, Naomichi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Communicability betweenness in complex networks

AU - Estrada, Ernesto

AU - Higham, Desmond J.

AU - Hatano, Naomichi

PY - 2009/3/1

Y1 - 2009/3/1

N2 - Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 036111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a proteinprotein interaction network.

AB - Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano [E. Estrada, N. Hatano, Phys. Rev. E 77 (2008) 036111]. Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a proteinprotein interaction network.

KW - centrality measures

KW - proteinprotein interactions

KW - communicability

KW - spectral graph theory

KW - conserved proteins

KW - linear response

KW - fréchet derivative

UR - http://arxiv.org/ftp/arxiv/papers/0905/0905.4102.pdf

U2 - 10.1016/j.physa.2008.11.011

DO - 10.1016/j.physa.2008.11.011

M3 - Article

VL - 388

SP - 764

EP - 774

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 - 5

ER -