Compute betweenness centrality for an undirected graph

Description

Compute betweenness centrality for an undirected graph

Usage

brandes.betweenness.centrality(g)

Arguments

Details

Brandes.betweenness.centrality computes the betweenness centrality of each vertex or each edge in the graph, using an algorithm by U. Brandes.

Betweenness centrality of a vertex v is calculated as follows: N_st(v) = no. of shortest paths from s to t that pass through v, N_st = no. of shortest paths from s to t, betweenness centrality of v = sum(N_st(v)/N_st) for all vertices s != v != t.

Betweenness centrality of an edge is calculated similarly.

The relative betweenness centrality for a vertex is to scale the betweenness centrality of the given vertex by 2/(n**2 - 3n + 2) where n is the no. of vertices in the graph.

Central point dominance measures the maximum betweenness of any vertex in the graph.

See documentation on brandes betweenness centrality in Boost Graph Library for more details.

Value

A list of

Author(s)

Li Long <li.long@isb-sib.ch>

References

Boost Graph Library ( www.boost.org/libs/graph/doc/index.html )

The Boost Graph Library: User Guide and Reference Manual; by Jeremy G. Siek, Lie-Quan Lee, and Andrew Lumsdaine; (Addison-Wesley, Pearson Education Inc., 2002), xxiv+321pp. ISBN 0-201-72914-8

See Also

betweenness.centrality.clustering

Examples

con <- file(system.file("XML/conn.gxl",package="RBGL"), open="r")
coex <- fromGXL(con)
close(con)
coex <- ugraph(coex)
brandes.betweenness.centrality(coex)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RBGL)
Loading required package: graph
Loading required package: BiocGenerics
Loading required package: parallel

Attaching package: 'BiocGenerics'

The following objects are masked from 'package:parallel':

    clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
    clusterExport, clusterMap, parApply, parCapply, parLapply,
    parLapplyLB, parRapply, parSapply, parSapplyLB

The following objects are masked from 'package:stats':

    IQR, mad, xtabs

The following objects are masked from 'package:base':

    Filter, Find, Map, Position, Reduce, anyDuplicated, append,
    as.data.frame, cbind, colnames, do.call, duplicated, eval, evalq,
    get, grep, grepl, intersect, is.unsorted, lapply, lengths, mapply,
    match, mget, order, paste, pmax, pmax.int, pmin, pmin.int, rank,
    rbind, rownames, sapply, setdiff, sort, table, tapply, union,
    unique, unsplit

> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/RBGL/betweenness.Rd_%03d_medium.png", width=480, height=480)
> ### Name: brandes.betweenness.centrality
> ### Title: Compute betweenness centrality for an undirected graph
> ### Aliases: brandes.betweenness.centrality
> ### Keywords: models
> 
> ### ** Examples
> 
> con <- file(system.file("XML/conn.gxl",package="RBGL"), open="r")
> coex <- fromGXL(con)
> close(con)
> coex <- ugraph(coex)
> brandes.betweenness.centrality(coex)
$betweenness.centrality.vertices
     A B C  D E H F G
[1,] 0 0 0 12 4 4 0 0

$edges
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] "A"  "A"  "A"  "B"  "B"  "C"  "D"  "D"  "E"  "E"   "E"   "H"   "H"   "F"  
[2,] "B"  "C"  "D"  "C"  "D"  "D"  "E"  "H"  "G"  "H"   "F"   "F"   "G"   "G"  

$betweenness.centrality.edges
           [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
centrality    1    1    5    1    5    5    8    8    3     1     3     3     3
           [,14]
centrality     1

$relative.betweenness.centrality.vertices
     A B C         D         E         H F G
[1,] 0 0 0 0.5714286 0.1904762 0.1904762 0 0

$dominance
[1] 0.5170068

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>