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## Re: [igraph] centralization again

 From: Simone Gabbriellini Subject: Re: [igraph] centralization again Date: Tue, 25 Nov 2008 00:12:14 +0100

```yes this does make sense!

I am having a look at Wasserman and Faust, and now I realize that the
implementation at pag 180 - the same you gave me some email ago - is
for undirected relation only... your last implementation solves my
problem.

thank you,
Simone

> Well, we will sort this centralization out, sooner of later.... I
> think it is just a question of definition. Your definition is fine for
> undirected graphs, among these the most centralized (according to
> degree) is the star.
>
> This one is a directed graph, however, so you probably want to count
> the incoming connections only. (Or maybe not? Again, a question of
> definition.) If you want to count the incoming edges for directed
> graphs, then the definition reads as
>
> centralization <- function(g)
> (sum(max(degree(g,mode="in"))-degree(g,mode="in")))/(vcount(g)-1)/(vcount(g)-2)
>
> If you want to count all edges, incoming and outgoing as well, then it is
>
> centralization <- function(g)
> (sum(max(degree(g))-degree(g)))/(2*vcount(g)-2)/(vcount(g)-2)
>
> Here we assume that there are at most two edges between a pair of
> vertices, at most one each direction. For graphs with multiple edges
> this definition fails as well.
>
> Does this make sense?
> Gabor
>
> On Mon, Nov 24, 2008 at 11:30 PM, Simone Gabbriellini
>> Dear Gabor,
>>
>> sorry to trouble you again with a centralization problem, but I am
>> experiencing a trouble with my graph.
>>
>> centralization<-(sum(max(degree(g))-degree(g))) / (vcount(g)-1) /
>> (vcount(g)-2)
>>
>> this is the adiacency matrix of my graph:
>>
>>   a b c d
>> a 0 1 1 1
>> b 1 0 0 0
>> c 1 0 0 0
>> d 1 0 0 0
>>
>> and this is a brief summary
>>
>>> summary(WOW)
>> Vertices: 4
>> Edges: 6
>> Directed: TRUE
>> No graph attributes.
>> Vertex attributes: id.
>> Edge attributes: weight, color.
>>
>> the surprise is that the result of centralization is 2... which is
>> pretty unusual for centralization...
>> I have others networks, and for them the code always runs ok, but with
>> this particular network, it seems not to work properly...
>>
>> any help, as usual, is more than welcome
>>
>> cheers,
>> Simone
>>
>>
>> _______________________________________________
>> igraph-help mailing list
>> http://lists.nongnu.org/mailman/listinfo/igraph-help
>>
>
>
>
> --
> Gabor Csardi <address@hidden>     UNIL DGM
>
>
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