[igraph] betweeness centrality for a directed weighted graph

[Jonas Richhardt]

Hi,

Fist of all I use the igraph package in R.
I struggle with the betweeness centrality funciton. First question is 
does that function resbects the weights of a graph.
I think it does not. If i use the general formula to calculate the 
betweeness centrality with the betweeness for the single knotes my 
results differ form what the
betweeness centrality function returns.

#### begin code

patchmat = 
cbind(c(0,0,0,0,0,1),c(0,0,1,0,0,0),c(0,1,0,0,0,1),c(0,0,0,0,1,1),c(0,0,0,1,0,1),c(1,0,1,1,1,0))
for (row in seq (1:6)){  ### some sort of normalising
    patchmat[row,] <- dat.raw[row,]/sum(dat.raw[row,])
    patchmat = matrix(data = patchmat, ncol = 6, nrow = 6)
  }

graph <- graph.adjacency(as.matrix(patchmat), mode="directed", 
weighted=TRUE)                 ### here we transform the adjacency 
matrix into a graph-object

betweenness(graph, v=V(graph), directed = TRUE, normalized = TRUE) ### 
returns 0.72

### but using the general formula
6*max(betweenness(graph, v=V(graph), directed = TRUE, normalized = 
TRUE))-sum(betweenness(graph, v=V(graph), directed = TRUE, normalized = 
TRUE)) ### returns 3.6

#### end code

Please help me to understand what happens here. The results differ by a 
factor of 5.

Thanks in review
Jonas