## Faster Evaluation of Shortest-Path Based Centrality Indices (2000)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Brandes00fasterevaluation,

author = {Ulrik Brandes},

title = {Faster Evaluation of Shortest-Path Based Centrality Indices},

year = {2000}

}

### OpenURL

### Abstract

Centrality indices are an important tool in network analysis, and many of them are derived from the set of all shortest paths of the underlying graph. The so-called betweenness centrality index is essential for the analysis of social networks, but most costly to compute. Currently, the fastest known algorithms require Theta(n³) time and Theta(n²) space, where n is the number of vertices. Motivated by the fast-growing need to compute centrality indices on large, yet very sparse, networks, new algorithms for betweenness are introduced in this paper. They require O(n + m) space and run in O(n(m + n)) or O(n(m + n log n)) time on unweighted or weighted graphs, respectively, where m is the number of edges. Since these algorithms simply augment single-source shortest-paths computations, all standard centrality indices based on shortest paths can now be computed uniformly in one framework. Experimental evidence is provided that this substantially increases the range of network...