# Normalize centrality measures

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


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

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

• so I can use Normalize to convert my vector in normalised vector Dec 20, 2014 at 23:44
• Take an arbitrary real vector then n = 10; Array[x, n] // Normalize // Norm // FullSimplify[#, Element[Array[x, n], Reals]] & gives 1 Dec 21, 2014 at 0:49

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.