## A measure of betweenness centrality based on random walks (2005)

Venue: | Social Networks |

Citations: | 155 - 0 self |

### BibTeX

@ARTICLE{Newman05ameasure,

author = {M. E. J. Newman},

title = {A measure of betweenness centrality based on random walks},

journal = {Social Networks},

year = {2005}

}

### Years of Citing Articles

### OpenURL

### Abstract

Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node has over the spread of information through the network. By counting only shortest paths, however, the conventional definition implicitly assumes that information spreads only along those shortest paths. Here we propose a betweenness measure that relaxes this assumption, including contributions from essentially all paths between nodes, not just the shortest, although it still gives more weight to short paths. The measure is based on random walks, counting how often a node is traversed by a random walk between two other nodes. We show how our measure can be calculated using matrix methods, and give some examples of its application to particular networks. 1

### Citations

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Citation Context ...itted from s to t, averaged over all s and t. 4 Maximum flow from a given s to all reachable targets t can be calculated in worst-case time O(m 2 ) using, for instance, the augmenting path algorithm (=-=Ahuja et al. 1993-=-), and hence the flow betweenness for all vertices can be calculated in time O(m 2 n). 5 In practical terms, one can think of flow betweenness as measuring the betweenness of vertices in a network in ... |

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Citation Context ... of our measure and prove that the two definitions are the same. The developments of this section follow similar lines to a previous presentation we have given on methods for hierarchical clustering (=-=Newman and Girvan 2003-=-). 2.1 A current flow analogy Consider, then, an electrical circuit created by placing a unit resistance on every edge of the network of interest, as shown in Fig. 2. One unit of current is injected i... |

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Citation Context ...hortest 3 Alternatively, bi may be normalized by dividing by its maximum possible value, which it achieves for a “star graph” in which one central vertex is connected to every other by a single edge (=-=Freeman 1979-=-).Betweenness and random walks 3 (a) C (b) A Group 1 Group 2 A B Group 1 B C Group 2 Figure 1: (a) Vertices A and B will have high (shortest-path) betweenness in this configuration, while vertex C wi... |

474 |
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Citation Context ...work researchers have introduced a large number of centrality indices, measures of the varying importance of the vertices in a network according to one criterion or another (Wasserman and Faust 1994; =-=Scott 2000-=-). These indices have proved of great value in the analysis and understanding of the roles played by actors in social networks, 1 as well as by vertices in networks of other types, including citation ... |

327 | A faster algorithm for betweenness centrality
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(Show Context)
Citation Context ...nness of a vertex measures how much flow will pass through that particular vertex. Betweenness can be calculated for all vertices in time O(mn) for a network with m edges and n vertices (Newman 2001; =-=Brandes 2001-=-). In most networks however, information (or anything else) does not flow only along geodesic paths (Stephenson and Zelen 1989; Freeman et al. 1991). News or a rumor or a message or a fad does not kno... |

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Citation Context ...l route to take to get from one place to another; more likely it wanders around more randomly, encountering who it will. And even in a case such as the famous small-world experiment of Milgram (1967; =-=Travers and Milgram 1969-=-), or its modern-day equivalent (Dodds et al. 2003), in which participants are explicitly instructed to get a message to a target by the most direct route possible, there is no evidence that people ar... |

173 |
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(Show Context)
Citation Context ...s, the betweenness of a vertex measures how much flow will pass through that particular vertex. Betweenness can be calculated for all vertices in time O(mn) for a network with m edges and n vertices (=-=Newman 2001-=-; Brandes 2001). In most networks however, information (or anything else) does not flow only along geodesic paths (Stephenson and Zelen 1989; Freeman et al. 1991). News or a rumor or a message or a fa... |

133 | Why social networks are different from other types of networks - Newman, Juyong - 2003 |

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Citation Context ...kely it wanders around more randomly, encountering who it will. And even in a case such as the famous small-world experiment of Milgram (1967; Travers and Milgram 1969), or its modern-day equivalent (=-=Dodds et al. 2003-=-), in which participants are explicitly instructed to get a message to a target by the most direct route possible, there is no evidence that people are especially successful in this task. Thus we woul... |

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Citation Context ...mn) for a network with m edges and n vertices (Newman 2001; Brandes 2001). In most networks however, information (or anything else) does not flow only along geodesic paths (Stephenson and Zelen 1989; =-=Freeman et al. 1991-=-). News or a rumor or a message or a fad does not know the ideal route to take to get from one place to another; more likely it wanders around more randomly, encountering who it will. And even in a ca... |

58 |
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Citation Context ...ples of applications of our betweenness measure to previously studied networks. First, we look at Padgett’s famous network of intermarriages between prominent families in early 15th century Florence (=-=Padgett and Ansell 1993-=-), depicted in Fig. 6. In Table 2, we rank the fifteen families by their random-walk betweenness, finding that the Medici come out well ahead of the competition, and in particular, they easily best th... |

54 |
Rethinking Centrality: Methods and Examples
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Citation Context ...for all vertices in time O(mn) for a network with m edges and n vertices (Newman 2001; Brandes 2001). In most networks however, information (or anything else) does not flow only along geodesic paths (=-=Stephenson and Zelen 1989-=-; Freeman et al. 1991). News or a rumor or a message or a fad does not know the ideal route to take to get from one place to another; more likely it wanders around more randomly, encountering who it w... |

17 | Random walks on complex networks - Noh, Rieger - 2004 |

15 | Risk network structure in the early epidemic phase of HIV transmission in Colorado Springs. Sexually Transmitted Infections 78(Supplement - Potterat, Phillips-Plummer, et al. - 2002 |

12 |
Betweenness centrality correlation in social networks
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(Show Context)
Citation Context ...rtex has a higher centrality in both of the networks. 3.2 Correlation with other measures Shortest-path betweenness is known to be strongly correlated with vertex degree in most networks (Nakao 1990; =-=Goh et al. 2003-=-), and it has been argued that this makes it a less useful measure. If the two are strongly correlated, then what is the point of going to the effort of calculating betweenness, when degree is almost ... |

5 |
Distribution of Measures of Centrality: Enumerated Distributions of Freeman's Graph Centrality Measures." Connections
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(Show Context)
Citation Context ...that this vertex has a higher centrality in both of the networks. 3.2 Correlation with other measures Shortest-path betweenness is known to be strongly correlated with vertex degree in most networks (=-=Nakao 1990-=-; Goh et al. 2003), and it has been argued that this makes it a less useful measure. If the two are strongly correlated, then what is the point of going to the effort of calculating betweenness, when ... |