### Abstract

In recent years, the increasing availability of data describing the dynamics of real-world systems led to a surge of interest in the complex networks of interactions that emerge from such systems. Several measures have been introduced to analyse these networks, and among them one of the most fundamental ones is vertex centrality, which quantifies the importance of a vertex within a graph. In this paper, we propose a novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity. More specifically, we measure the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph. More specifically, we find that the centrality of a vertex v can be broken down in two parts: (1) one which is negatively correlated with the degree centrality of v, and (2) one which depends on the emergence of non-trivial structures in the graph when v is disconnected from the rest of the graph. Finally, we evaluate our centrality measure on a number of real-world as well as synthetic networks, and we compare it against a set of commonly used alternative measures.

Original language | English |
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Title of host publication | Graph-based representations in pattern recognition : 11th IAPR-TC-15 international workshop, GbRPR 2017. Proceedings |

Editors | Pasquale Foggia, Cheng-Lin Liu, Mario Vento |

Place of Publication | Cham (CH) |

Publisher | Springer |

Pages | 154-164 |

Number of pages | 11 |

ISBN (Electronic) | 978-3-319-58961-9 |

ISBN (Print) | 978-3-319-58960-2 |

DOIs | |

Publication status | Published - 2017 |

Event | 11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017 - Anacapri, Italy Duration: 16 May 2017 → 18 May 2017 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 10310 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017 |
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Country | Italy |

City | Anacapri |

Period | 16/05/17 → 18/05/17 |

### Fingerprint

### Keywords

- complex networks
- quantum Information
- vertex centrality

### Cite this

*Graph-based representations in pattern recognition : 11th IAPR-TC-15 international workshop, GbRPR 2017. Proceedings*(pp. 154-164). (Lecture Notes in Computer Science; Vol. 10310). Cham (CH): Springer. https://doi.org/10.1007/978-3-319-58961-9_14

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*Graph-based representations in pattern recognition : 11th IAPR-TC-15 international workshop, GbRPR 2017. Proceedings.*Lecture Notes in Computer Science, vol. 10310, Springer, Cham (CH), pp. 154-164, 11th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition, GbRPR 2017 , Anacapri, Italy, 16/05/17. https://doi.org/10.1007/978-3-319-58961-9_14

**Measuring vertex centrality using the Holevo quantity.** / Rossi, Luca; Torsello, Andrea.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Measuring vertex centrality using the Holevo quantity

AU - Rossi, Luca

AU - Torsello, Andrea

PY - 2017

Y1 - 2017

N2 - In recent years, the increasing availability of data describing the dynamics of real-world systems led to a surge of interest in the complex networks of interactions that emerge from such systems. Several measures have been introduced to analyse these networks, and among them one of the most fundamental ones is vertex centrality, which quantifies the importance of a vertex within a graph. In this paper, we propose a novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity. More specifically, we measure the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph. More specifically, we find that the centrality of a vertex v can be broken down in two parts: (1) one which is negatively correlated with the degree centrality of v, and (2) one which depends on the emergence of non-trivial structures in the graph when v is disconnected from the rest of the graph. Finally, we evaluate our centrality measure on a number of real-world as well as synthetic networks, and we compare it against a set of commonly used alternative measures.

AB - In recent years, the increasing availability of data describing the dynamics of real-world systems led to a surge of interest in the complex networks of interactions that emerge from such systems. Several measures have been introduced to analyse these networks, and among them one of the most fundamental ones is vertex centrality, which quantifies the importance of a vertex within a graph. In this paper, we propose a novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity. More specifically, we measure the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph. More specifically, we find that the centrality of a vertex v can be broken down in two parts: (1) one which is negatively correlated with the degree centrality of v, and (2) one which depends on the emergence of non-trivial structures in the graph when v is disconnected from the rest of the graph. Finally, we evaluate our centrality measure on a number of real-world as well as synthetic networks, and we compare it against a set of commonly used alternative measures.

KW - complex networks

KW - quantum Information

KW - vertex centrality

UR - http://www.scopus.com/inward/record.url?scp=85019596244&partnerID=8YFLogxK

UR - https://link.springer.com/chapter/10.1007%2F978-3-319-58961-9_14

U2 - 10.1007/978-3-319-58961-9_14

DO - 10.1007/978-3-319-58961-9_14

M3 - Conference contribution

AN - SCOPUS:85019596244

SN - 978-3-319-58960-2

T3 - Lecture Notes in Computer Science

SP - 154

EP - 164

BT - Graph-based representations in pattern recognition : 11th IAPR-TC-15 international workshop, GbRPR 2017. Proceedings

A2 - Foggia, Pasquale

A2 - Liu, Cheng-Lin

A2 - Vento, Mario

PB - Springer

CY - Cham (CH)

ER -