betweenness centrality question(R interface)

Asked by tear2001

I am curious about the result output of betweenness centrality function.

In package description:
The vertex and edge betweenness are (roughly) defined by "the number of geodesics (shortest paths)" going through a vertex or an edge.

however, when I try the example in document:
g <- random.graph.game(10, 3/10)
[0] 1 -- 3
[1] 2 -- 3
[2] 0 -- 4
[3] 3 -- 4
[4] 2 -- 5
[5] 4 -- 6
[6] 5 -- 6
[7] 1 -- 7
[8] 2 -- 7
[9] 4 -- 7
[10] 5 -- 7
[11] 0 -- 8
[12] 2 -- 8
[13] 5 -- 8
[14] 7 -- 8
[15] 3 -- 9
[16] 8 -- 9
betweenness(g,v=V(g))
[1] 0.5000000 0.3333333 1.8333333 5.1666667 6.1666667 3.3333333 0.5000000
[8] 5.8333333 6.8333333 0.5000000

The result is not "the number of geodesics (shortest paths)" because I think it should be integer number.
Do I mis-understand the output?

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Tamás Nepusz
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Best Tamás Nepusz (ntamas) said :
#1

That's why the documentation says that the betweenness centrality is "roughly" the number of shortest paths going through a vertex or an edge. The problem is that there could exist two vertices A and B with multiple shortest paths between them. If there are k shortest paths between A and B, each of them counts only as 1/k.

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tear2001 (gnerv) said :
#2

Thanks Tamás Nepusz, that solved my question.