### Abstract

We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering one can independently tune the power law exponent τ > 2 of the degree distribution and a parameter δ > 1 determining the decay rate of the probability of long edges. We argue that the network is robust if (Formula Presented.), but fails to be robust if (Formula Presented.). Hence robustness depends not only on the power-law exponent but also on the clustering features of the network.

Original language | English |
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Title of host publication | Algorithms and Models for the Web Graph |

Subtitle of host publication | Proceedings of 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015 |

Editors | D. F. Gleich, J. Komjathy, N. Litvak |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 3-14 |

Number of pages | 12 |

ISBN (Print) | 9783319267838 |

DOIs | |

Publication status | Published - 9 Dec 2015 |

Event | 12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015 - Eindhoven, Netherlands Duration: 10 Dec 2015 → 11 Dec 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9479 |

### Conference

Conference | 12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015 |
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Country | Netherlands |

City | Eindhoven |

Period | 10/12/15 → 11/12/15 |

### Fingerprint

### Keywords

- Barabasi-Albert model
- Clustering
- Geometric random graph
- Giant component
- Power law
- Preferential attachment
- Resilience
- Robustness
- Scale-free network

### Cite this

*Algorithms and Models for the Web Graph: Proceedings of 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015*(pp. 3-14). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9479). Switzerland: Springer. https://doi.org/10.1007/978-3-319-26784-5_1

**Robustness of spatial preferential attachment networks.** / Jacob, Emmanuel; Morters, Peter.

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

*Algorithms and Models for the Web Graph: Proceedings of 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9479, Springer, Switzerland, pp. 3-14, 12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015, Eindhoven, Netherlands, 10/12/15. https://doi.org/10.1007/978-3-319-26784-5_1

}

TY - GEN

T1 - Robustness of spatial preferential attachment networks

AU - Jacob, Emmanuel

AU - Morters, Peter

PY - 2015/12/9

Y1 - 2015/12/9

N2 - We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering one can independently tune the power law exponent τ > 2 of the degree distribution and a parameter δ > 1 determining the decay rate of the probability of long edges. We argue that the network is robust if (Formula Presented.), but fails to be robust if (Formula Presented.). Hence robustness depends not only on the power-law exponent but also on the clustering features of the network.

AB - We study robustness under random attack for a class of networks, in which new nodes are given a spatial position and connect to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering one can independently tune the power law exponent τ > 2 of the degree distribution and a parameter δ > 1 determining the decay rate of the probability of long edges. We argue that the network is robust if (Formula Presented.), but fails to be robust if (Formula Presented.). Hence robustness depends not only on the power-law exponent but also on the clustering features of the network.

KW - Barabasi-Albert model

KW - Clustering

KW - Geometric random graph

KW - Giant component

KW - Power law

KW - Preferential attachment

KW - Resilience

KW - Robustness

KW - Scale-free network

UR - http://www.scopus.com/inward/record.url?scp=84951870631&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-26784-5_1

DO - 10.1007/978-3-319-26784-5_1

M3 - Conference contribution

SN - 9783319267838

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 3

EP - 14

BT - Algorithms and Models for the Web Graph

A2 - Gleich, D. F.

A2 - Komjathy, J.

A2 - Litvak, N.

PB - Springer

CY - Switzerland

ER -