## Centrality estimation in large networks (2007)

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Venue: | INTL. JOURNAL OF BIFURCATION AND CHAOS, SPECIAL ISSUE ON COMPLEX NETWORKS’ STRUCTURE AND DYNAMICS |

Citations: | 29 - 0 self |

### BibTeX

@INPROCEEDINGS{Brandes07centralityestimation,

author = {Ulrik Brandes and Christian Pich},

title = { Centrality estimation in large networks},

booktitle = {INTL. JOURNAL OF BIFURCATION AND CHAOS, SPECIAL ISSUE ON COMPLEX NETWORKS’ STRUCTURE AND DYNAMICS},

year = {2007},

publisher = {}

}

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### Abstract

Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.

### Citations

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Citation Context ...asures is based on feedback, i.e. the centrality of a vertex directly influences that of its neighbors. Well-known members of this class are eigenvector centrality [Bonacich 1972], Google’s PageRank [=-=Brin and Page 1998-=-], and hubs & authorities [Kleinberg 1999]. For most of these measures, generalizations have been proposed for directed, non-simple, weighted, and unconnected graphs, and there is a similar range of i... |

2901 | Authoritative sources in a hyperlinked environment
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Citation Context ...ity of a vertex directly influences that of its neighbors. Well-known members of this class are eigenvector centrality [Bonacich 1972], Google’s PageRank [Brin and Page 1998], and hubs & authorities [=-=Kleinberg 1999-=-]. For most of these measures, generalizations have been proposed for directed, non-simple, weighted, and unconnected graphs, and there is a similar range of indices that value the importance of edges... |

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321 | A faster algorithm for betweenness centrality
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Citation Context ...air s, t ∈ V on v ∈ V and summing out all targets t, cB(v) = � s�=v�=t σ(s, t|v) σ (s, t) = � s�=v�=t δ(s, t|v) = � δ(s|v) , where δ(s|v) = � t�=v δ(s, t|v) is the one-sided dependency of s on v. In [=-=Brandes 2001-=-] it is shown how to compute the one-sided dependencies of all v ∈ V for a given s ∈ V by solving an SSSP. Therefore, betweenness centrality can be computed in the same asymptotic time bounds, and in ... |

164 | The degree sequence of a scale-free random graph process”, Random Structures and Algorithms,Volume 18 - Bollobás, Riordan, et al. |

152 | A measure of betweenness centrality based on random walks
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Citation Context ...r use maximum network flow instead of shortest paths [Freeman et al. 1991]. Natural variants of closeness and betweenness are also obtained by replacing spread along shortest paths with current flow [=-=Newman 2005-=-, Brandes and Fleischer 2005]. A different class of measures is based on feedback, i.e. the centrality of a vertex directly influences that of its neighbors. Well-known members of this class are eigen... |

141 |
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Citation Context ...cher 2005]. A different class of measures is based on feedback, i.e. the centrality of a vertex directly influences that of its neighbors. Well-known members of this class are eigenvector centrality [=-=Bonacich 1972-=-], Google’s PageRank [Brin and Page 1998], and hubs & authorities [Kleinberg 1999]. For most of these measures, generalizations have been proposed for directed, non-simple, weighted, and unconnected g... |

123 | Sampling
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Citation Context ...at the variance in quality over different runs is very small. An alternative strategy to improve over our estimates is to use more sophisticated techniques than our simple random sampling estimators [=-=Thompson 2002-=-]. While we have not performed a thorough study, it seems, though, that reasonable and efficient estimators are difficult to design and subject to the same problems exhibited by skewed pivot selection... |

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Citation Context ...center problem in facility location, in which the goal is to findsEstimating Centrality 10 a set of k vertices, the centers, such that the distance from any vertex to the closest center is minimized [=-=Hochbaum and Shmoys 1986-=-]. MaxSum Intuitively, the sum of distances is an even better indicator of how badly covered a vertex is by the current set of pivots. We may therefore wish to select the next pivot pi from Vi by maxi... |

49 |
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Citation Context ...d (see [Brandes and Erlebach 2005] for an overview). Two of the indices most commonly used in the social sciences are closeness centrality [Beauchamp 1965, Sabidussi 1966] and betweenness centrality [=-=Anthonisse 1971-=-, Freeman 1977]. Both are based on shortest-path distances, but while a node has high closeness centrality if its total (and therefore also average) distance to all other vertices is small, a high bet... |

36 | Fast approximation of centrality - Eppstein, Wang - 2001 |

36 |
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Citation Context ...indices that are based on similar notions of importance. For instance, we can replace the sum of distances in closenesssEstimating Centrality 5 centrality by the maximum distance to any other vertex [=-=Harary and Hage 1995-=-], or subtract each distance from an upper bound rather than taking the inverse [Botagfogo et al. 1992, Valente et al. 1998]. Variants of betweenness count all shortest paths equally [Shimbel 1953] or... |

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31 |
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Citation Context ...ry and Hage 1995], or subtract each distance from an upper bound rather than taking the inverse [Botagfogo et al. 1992, Valente et al. 1998]. Variants of betweenness count all shortest paths equally [=-=Shimbel 1953-=-] or use maximum network flow instead of shortest paths [Freeman et al. 1991]. Natural variants of closeness and betweenness are also obtained by replacing spread along shortest paths with current flo... |

28 |
An Improved Index of Centrality
- Beauchamp
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(Show Context)
Citation Context ...suring the structural importance of nodes in a network abound (see [Brandes and Erlebach 2005] for an overview). Two of the indices most commonly used in the social sciences are closeness centrality [=-=Beauchamp 1965-=-, Sabidussi 1966] and betweenness centrality [Anthonisse 1971, Freeman 1977]. Both are based on shortest-path distances, but while a node has high closeness centrality if its total (and therefore also... |

22 | Centrality measures based on current flow
- Brandes, Fleischer
- 2005
(Show Context)
Citation Context ... network flow instead of shortest paths [Freeman et al. 1991]. Natural variants of closeness and betweenness are also obtained by replacing spread along shortest paths with current flow [Newman 2005, =-=Brandes and Fleischer 2005-=-]. A different class of measures is based on feedback, i.e. the centrality of a vertex directly influences that of its neighbors. Well-known members of this class are eigenvector centrality [Bonacich ... |

17 | Efficient generation of large random networks - Batagelj, Brandes |

13 |
A set of measures of centrality based upon betweeness
- Freeman
- 1977
(Show Context)
Citation Context ...nd Erlebach 2005] for an overview). Two of the indices most commonly used in the social sciences are closeness centrality [Beauchamp 1965, Sabidussi 1966] and betweenness centrality [Anthonisse 1971, =-=Freeman 1977-=-]. Both are based on shortest-path distances, but while a node has high closeness centrality if its total (and therefore also average) distance to all other vertices is small, a high betweenness centr... |

12 |
Centrality indices
- Koschützki, Lehmann, et al.
- 2005
(Show Context)
Citation Context ...under grant Br 2158/2-3 1sEstimating Centrality 2 1 Introduction An essential tool in the analysis of complex networks are centrality indices defined on the vertices or edges of the underlying graph [=-=Koschützki et al. 2005-=-a,b]. Depending on the type of network studied, they are proxies for the structural importance of an element for the overall functioning of the network. Many popular centrality indices are based on sh... |

8 |
Practical Issues and Algorithms for Analyzing Terrorist Networks
- Carpenter, Karakostas, et al.
(Show Context)
Citation Context ...e discrete concepts of centrality based on shortest paths, these are not applicable. In fact, approximation of betweenness centrality (defined below) is stated as an important open problem, e.g., in [=-=Carpenter et al. 2002-=-]. We here present an experimental study of estimators for the two most commonly used shortest-path centralities, closeness and betweenness. The estimates are based on a restricted number of single-so... |

3 |
Satellite exchange in the Baltimore needle exchange program. Public Health Reports
- Valente, Foreman, et al.
- 1998
(Show Context)
Citation Context ...mating Centrality 5 centrality by the maximum distance to any other vertex [Harary and Hage 1995], or subtract each distance from an upper bound rather than taking the inverse [Botagfogo et al. 1992, =-=Valente et al. 1998-=-]. Variants of betweenness count all shortest paths equally [Shimbel 1953] or use maximum network flow instead of shortest paths [Freeman et al. 1991]. Natural variants of closeness and betweenness ar... |

2 |
Advanced centrality concepts
- Koschützki, Lehmann, et al.
- 2005
(Show Context)
Citation Context ...under grant Br 2158/2-3 1sEstimating Centrality 2 1 Introduction An essential tool in the analysis of complex networks are centrality indices defined on the vertices or edges of the underlying graph [=-=Koschützki et al. 2005-=-a,b]. Depending on the type of network studied, they are proxies for the structural importance of an element for the overall functioning of the network. Many popular centrality indices are based on sh... |

1 |
Network models
- Baumann, Stiller
- 2005
(Show Context)
Citation Context ...order of 1,000 vertices and 10,000 edges). See Tab. 2 for a summary. 5.1 Data place Table 2 about here There are numerous models for generating random graphs with specific structural characteristics [=-=Baumann and Stiller 2005-=-]. We have selected three of the more common ones. Random Graphs. The basic random graph model of Gilbert [1959] 1 is defined by two parameters, the number of vertices n and an edge probability 0 < p ... |

1 |
Estimating Centrality 17
- Botagfogo, Rivlin, et al.
- 1992
(Show Context)
Citation Context ...ances in closenesssEstimating Centrality 5 centrality by the maximum distance to any other vertex [Harary and Hage 1995], or subtract each distance from an upper bound rather than taking the inverse [=-=Botagfogo et al. 1992-=-, Valente et al. 1998]. Variants of betweenness count all shortest paths equally [Shimbel 1953] or use maximum network flow instead of shortest paths [Freeman et al. 1991]. Natural variants of closene... |

1 |
Estimating Centrality 18
- Freeman, Borgatti, et al.
- 1991
(Show Context)
Citation Context ...er than taking the inverse [Botagfogo et al. 1992, Valente et al. 1998]. Variants of betweenness count all shortest paths equally [Shimbel 1953] or use maximum network flow instead of shortest paths [=-=Freeman et al. 1991-=-]. Natural variants of closeness and betweenness are also obtained by replacing spread along shortest paths with current flow [Newman 2005, Brandes and Fleischer 2005]. A different class of measures i... |

1 |
Estimating Centrality 19
- Sabidussi
- 1966
(Show Context)
Citation Context ...tural importance of nodes in a network abound (see [Brandes and Erlebach 2005] for an overview). Two of the indices most commonly used in the social sciences are closeness centrality [Beauchamp 1965, =-=Sabidussi 1966-=-] and betweenness centrality [Anthonisse 1971, Freeman 1977]. Both are based on shortest-path distances, but while a node has high closeness centrality if its total (and therefore also average) distan... |