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How I can normalise centrality measures? Can I use Normalize function? I give example of unnormalized measures

g = GridGraph[{5, 5}];  
ClosenessCentrality[g] // Short  
BetweennessCentrality[g] // Short  
DegreeCentrality[g] // Short  

Thanks in advance

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  • $\begingroup$ Everybody any idea? $\endgroup$ Dec 20, 2014 at 17:05
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    $\begingroup$ What do you mean by "normalize" here? Can you define it? $\endgroup$
    – Szabolcs
    Dec 20, 2014 at 23:21
  • $\begingroup$ measures between 0 and 1 $\endgroup$ Dec 20, 2014 at 23:37
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    $\begingroup$ So why don't you just divide by the Maximum then? $\endgroup$
    – Szabolcs
    Dec 21, 2014 at 2:35

2 Answers 2

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Normalize will give you vectors whose Norm is one.

g = GridGraph[{5, 5}];

ClosenessCentrality[g] // Normalize // Norm

1.

BetweennessCentrality[g] // Normalize // Norm

1.

DegreeCentrality[g] // Normalize // Norm

1

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  • $\begingroup$ so I can use Normalize to convert my vector in normalised vector $\endgroup$ Dec 20, 2014 at 23:44
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    $\begingroup$ Take an arbitrary real vector then n = 10; Array[x, n] // Normalize // Norm // FullSimplify[#, Element[Array[x, n], Reals]] & gives 1 $\endgroup$
    – Bob Hanlon
    Dec 21, 2014 at 0:49
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You just has to use the definition of normalized centrality measures, for example, to betweenness centrality you must divide the vector by (n-1)(n-2) for the undirected case.

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