# A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks

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## Abstract

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## 1. Introduction

## 2. Model Description

## 3. Performance Evaluation

## 4. Conclusions and Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**The influence spread with different $k$ at time $t$. The results are obtained by using the entropy-based centrality in the four weighted networks including: (

**a**) adolescent health; (

**b**) US airports; (

**c**) Bible, and (

**d**) Hep-th, respectively.

**Figure 5.**The influence spread with different $k$ in the four weighted networks including: (

**a**) adolescent health, (

**b**) US airports, (

**c**) Bible, and (

**d**) Hep-th, respectively. The results are obtained by using the entropy-based centrality, degree centrality, betweenness centrality, and closeness centrality, respectively.

Between Two Airports | The Number of Airlines | Between two Airports | The Number of Airlines |
---|---|---|---|

$A\to B$ | 5 | $E\to B$ | 3 |

$A\to D$ | 1 | $E\to C$ | 3 |

$A\to F$ | 3 | $E\to D$ | 4 |

$B\to A$ | 4 | $E\to F$ | 2 |

$B\to C$ | 2 | $E\to G$ | 1 |

$B\to D$ | 3 | $F\to A$ | 1 |

$B\to E$ | 3 | $F\to G$ | 3 |

$C\to B$ | 4 | $F\to E$ | 2 |

$C\to E$ | 2 | $G\to E$ | 1 |

$C\to H$ | 5 | $G\to F$ | 1 |

$D\to A$ | 2 | $G\to H$ | 2 |

$D\to B$ | 5 | $H\to C$ | 1 |

$D\to E$ | 4 | $H\to G$ | 4 |

Node | $\mathit{D}{\mathit{C}}_{\mathit{i}}^{\mathit{i}\mathit{n}}$ | $\mathit{D}{\mathit{C}}_{\mathit{i}}^{\mathit{o}\mathit{u}\mathit{t}}$ | $\mathit{S}\mathit{D}{\mathit{C}}_{\mathit{i}}$ |
---|---|---|---|

B | 4 | 4 | 8 |

A | 2 | 2 | 4 |

C | 2 | 2 | 4 |

D | 3 | 3 | 6 |

E | 3 | 3 | 6 |

Node | Local Influence | Indirect Influence | Total Influence |
---|---|---|---|

A | 0.4736 | 0.2625 | 0.3892 |

B | 0.6273 | 0.3713 | 0.5249 |

C | 0.4955 | 0.3080 | 0.4205 |

D | 0.5073 | 0.3283 | 0.4357 |

E | 0.6956 | 0.3619 | 0.5521 |

F | 0.4930 | 0.2915 | 0.4124 |

G | 0.5004 | 0.2987 | 0.4197 |

H | 0.3110 | 0.2323 | 0.2795 |

Node | No. |
---|---|

E | 1 |

B | 2 |

D | 3 |

C | 4 |

G | 5 |

F | 6 |

A | 7 |

H | 8 |

Networks | $\mathit{n}$ | $\mathit{m}$ | $\mathit{c}$ ^{1} | $\mathit{A}\mathit{D}$ ^{2} |
---|---|---|---|---|

Adolescent health | 2539 | 12,969 | 14.2% | 10.216 (overall) |

US airports | 1574 | 28,236 | 38.4% | 35.878 (overall) |

Bible | 1773 | 9131 | 16.3% | 18.501 |

Hep-th | 8361 | 15,757 | 32.7% | 3.768 |

^{1}$c$ denotes the clustering coefficient.

^{2}$AD$ represents average degree.

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**MDPI and ACS Style**

Qiao, T.; Shan, W.; Yu, G.; Liu, C.
A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks. *Entropy* **2018**, *20*, 261.
https://doi.org/10.3390/e20040261

**AMA Style**

Qiao T, Shan W, Yu G, Liu C.
A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks. *Entropy*. 2018; 20(4):261.
https://doi.org/10.3390/e20040261

**Chicago/Turabian Style**

Qiao, Tong, Wei Shan, Ganjun Yu, and Chen Liu.
2018. "A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks" *Entropy* 20, no. 4: 261.
https://doi.org/10.3390/e20040261