### Abstract

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n^{2} log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worstcase time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs. Our approximation algorithm is based on an adaptive sampling technique that significantly reduces the number of single-source shortest path computations for vertices with high centrality. We conduct an extensive experimental study on real-world graph instances, and observe that our random sampling algorithm gives very good betweenness approximations for biological networks, road networks and web crawls.

Original language | English (US) |
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Title of host publication | Algorithms and Models for the Web-Graph - 5th International Workshop, WAW 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 124-137 |

Number of pages | 14 |

ISBN (Print) | 9783540770039 |

DOIs | |

State | Published - 2007 |

Event | 5th Workshop on Algorithms and Models for the Web-Graph, WAW 2007 - San Diego, CA, United States Duration: Dec 11 2007 → Dec 12 2007 |

### 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 | 4863 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th Workshop on Algorithms and Models for the Web-Graph, WAW 2007 |
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Country | United States |

City | San Diego, CA |

Period | 12/11/07 → 12/12/07 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Models for the Web-Graph - 5th International Workshop, WAW 2007, Proceedings*(pp. 124-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4863 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-77004-6_10