### 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 |

Pages | 124-137 |

Number of pages | 14 |

Volume | 4863 LNCS |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Models for the Web-Graph - 5th International Workshop, WAW 2007, Proceedings*(Vol. 4863 LNCS, pp. 124-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4863 LNCS).

}

*Algorithms and Models for the Web-Graph - 5th International Workshop, WAW 2007, Proceedings.*vol. 4863 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4863 LNCS, pp. 124-137, 5th Workshop on Algorithms and Models for the Web-Graph, WAW 2007, San Diego, CA, United States, 12/11/07.

**Approximating betweenness centrality.** / Bader, David A.; Kintali, Shiva; Madduri, Kamesh; Mihail, Milena.

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

TY - GEN

T1 - Approximating betweenness centrality

AU - Bader, David A.

AU - Kintali, Shiva

AU - Madduri, Kamesh

AU - Mihail, Milena

PY - 2007

Y1 - 2007

N2 - 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 + n2 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.

AB - 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 + n2 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.

UR - http://www.scopus.com/inward/record.url?scp=38149071742&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149071742&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38149071742

SN - 9783540770039

VL - 4863 LNCS

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

SP - 124

EP - 137

BT - Algorithms and Models for the Web-Graph - 5th International Workshop, WAW 2007, Proceedings

ER -