### Abstract

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

Pages | 4317-4328 |

Number of pages | 12 |

Journal | Linear Algebra and its Applications |

Volume | 436 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Jun 2012 |

### Fingerprint

### Keywords

- matrix functions
- Euclidean distance
- graph spectrum
- graph distance
- communicability

### Cite this

*Linear Algebra and its Applications*,

*436*(11), 4317-4328. https://doi.org/10.1016/j.laa.2012.01.017

}

*Linear Algebra and its Applications*, vol. 436, no. 11, pp. 4317-4328. https://doi.org/10.1016/j.laa.2012.01.017

**The communicability distance in graphs.** / Estrada, Ernesto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The communicability distance in graphs

AU - Estrada, Ernesto

PY - 2012/6/1

Y1 - 2012/6/1

N2 - Let G be a simple connected graph with adjacency matrix A. The communicabilityGpq between two nodes p and q of the graph is defined as the pq-entry of G=exp(A). We prove here that ξp,q=(Gpp+Gqq-2Gpq)1/2 is a Euclidean distance and give expressions for it in paths, cycles, stars and complete graphs with n nodes. The sum of all communicabilitydistances in a graph is introduced as a new graph invariant ϒ(G). We compare this index with the Wiener and Kirchhoff indices of graphs and conjecture about the graphs with maximum and minimum values of this index.

AB - Let G be a simple connected graph with adjacency matrix A. The communicabilityGpq between two nodes p and q of the graph is defined as the pq-entry of G=exp(A). We prove here that ξp,q=(Gpp+Gqq-2Gpq)1/2 is a Euclidean distance and give expressions for it in paths, cycles, stars and complete graphs with n nodes. The sum of all communicabilitydistances in a graph is introduced as a new graph invariant ϒ(G). We compare this index with the Wiener and Kirchhoff indices of graphs and conjecture about the graphs with maximum and minimum values of this index.

KW - matrix functions

KW - Euclidean distance

KW - graph spectrum

KW - graph distance

KW - communicability

UR - http://www.scopus.com/inward/record.url?scp=84863320828&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2012.01.017

DO - 10.1016/j.laa.2012.01.017

M3 - Article

VL - 436

SP - 4317

EP - 4328

JO - Linear Algebra and its Applications

T2 - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 11

ER -