### Abstract

graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of the

edges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.

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

Pages | 692-715 |

Number of pages | 24 |

Journal | SIAM Review |

Volume | 58 |

Issue number | 4 |

DOIs | |

Publication status | Published - 3 Nov 2016 |

### Fingerprint

### Keywords

- distance
- graph planarity
- Euclidean
- complex network
- communicability
- graph distance

### Cite this

*SIAM Review*,

*58*(4), 692-715. https://doi.org/10.1137/141000555

}

*SIAM Review*, vol. 58, no. 4, pp. 692-715. https://doi.org/10.1137/141000555

**Communicability angle and the spatial efficiency of networks.** / Estrada, Ernesto; Hatano, Naomichi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Communicability angle and the spatial efficiency of networks

AU - Estrada, Ernesto

AU - Hatano, Naomichi

N1 - First Published in SIAM Review in Vol 58(4) 2016, published by the Society for Industrial and Applied Mathematics (SIAM) “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”

PY - 2016/11/3

Y1 - 2016/11/3

N2 - We introduce the concept of communicability angle between a pair of nodes in agraph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of theedges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.

AB - We introduce the concept of communicability angle between a pair of nodes in agraph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of theedges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.

KW - distance

KW - graph planarity

KW - Euclidean

KW - complex network

KW - communicability

KW - graph distance

UR - http://epubs.siam.org/journal/siread

U2 - 10.1137/141000555

DO - 10.1137/141000555

M3 - Article

VL - 58

SP - 692

EP - 715

JO - SIAM Review

T2 - SIAM Review

JF - SIAM Review

SN - 0036-1445

IS - 4

ER -