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## Re: [igraph] Betweennes centrality (maximum and normalization)

 From: Colin Garroway Subject: Re: [igraph] Betweennes centrality (maximum and normalization) Date: Wed, 10 Feb 2010 11:19:31 -0500

Maybe something like this for normalization in R?  From the R recipes on the igraph wiki (http://igraph.wikidot.com/r-recipes#toc1).

``````centrality.norm<-function(graph,type=c("degree","closeness","betweenness"),centralization=FALSE)
{        result<-NA    g<-graph    cent<-centralization    if (!is.igraph(g)) {stop("Not a graph object")}    if (type[[1]] == "degree") {        if (!cent) result <- degree(g)/(vcount(g)-1)
else result <- (sum(max(degree(g))-degree(g)))/((vcount(g)-1)*(vcount(g)-2))}    else if (type[[1]] == "betweenness") {        temp <- 2*betweenness(g)/((vcount(g)-1)*(vcount(g)-2))        if (!cent) result <- temp
else  result <- sum(max(temp)-temp)/(vcount(g)-1)}    else if (type[[1]] == "closeness") {        if (!cent) result <- closeness(g)        else result <- (2*vcount(g)-3)*(sum(max(closeness(g))-closeness(g)))/((vcount(g)-1)*(vcount(g)-2))}
else {stop("this type is unavailable or mispelled")}    return(result)}``````

Colin

On 10 February 2010 11:12, Gábor Csárdi wrote:
Stefan, I am not sure that I understand your questions correctly, but
I think Freeman's paper might answer them:

Centrality in social networks conceptual clarification
Linton C. Freeman
Social Networks, 1979

Gabor

ps. google for it to get a PDF if you don't have sciencedirect access

On Wed, Feb 10, 2010 at 5:05 PM, Stefan Kroeger <address@hidden> wrote:
> Hi,
>
> I hope it's okay to ask a pretty special question to betweenes
> centrality (BC) and not directly related to igraph.
>
> (mention: I deal with the node-related BC in undirected graphs.)
>
> my two problems/questions are:
> (i) Is the highest measure BC of network, also the theoretical hightest
> reachable (maximum) BC for the graph?
>
> (ii) Is there a way to normalize the betweennes centrality measures to
> be able to compare between different graph?
>
>
> thanks a lot
> Stefan
>
>
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>

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Colin Garroway (PhD candidate)
Wildlife Research and Development Section
Ontario Ministry of Natural Resources
Trent University, DNA Building
2140 East Bank Drive
Peterborough, ON, K9J 7B8