[igraph] Understanding centralization betweenness

[Antoniazzi Marco]

Hi all,

I have a graph object 'g' with 14 nodes, edges are directed and weighted.

I would like to calculate centralization betweenness for the graph-level. If I write the code for the centralization I get the following results:

> c <- centralization.betweenness(centrg, directed=TRUE)

> c

$res

 [1]  0.2777778  4.7396825  2.1000000  0.9619048  3.4444444  0.3333333  7.5706349  8.3134921

 [9]  2.0563492  0.1111111  1.9428571  3.7396825 10.6619048  6.7468254

$centralization

[1] 0.04746877

$theoretical_max

[1] 2028

For what I understand the node-level indexes should be the betweenness calculated for each node? Is that right?

If yes, I want to check using the betweenness formula and I get the following:

z<- betweenness (g, directed =TRUE, weights= E(g)$weight)

> z

      X.3.     X.363.    X.1807.    X.1831.    X.1841.    X.1851.    X.2034.    X.3736.    X.4058. 

18.4166667  0.3333333 15.0333333 14.2916667  4.0583333  0.6250000  5.1166667  6.0333333 13.8333333 

   X.4396.   X.12882.   X.13017.   X.14075.   X.14937. 

 8.3166667 24.6500000  4.0000000 11.4833333 17.9000000 

where X.# are the codes for the nodes and 18.41.... etc the betweenness scores.

Can you help me interpret these results or to fix any mistake?

Also, what if I just want to get the $centralization using the centralization formula as an output? I need to write just that value to compare multiple networks.

thank you very much

Marko