[igraph] Centrality measure in igraph

[Mathieu Ferry]

Dear all, 

I am trying to apply some centrality measures to a network. 

I find that one node has a degree of 11, which is relatively high, 

but when I compute alpha centrality (alpha = 0.5 , exo= 0.5), I find a measure that is lower than this (1.875). 

I don't understand how this can be possible, whether it is theoretically possible actually... 

I mean, how can my alpha centrality measure be lower than 11*0.5 = 5.5? Shouldn't it be 11*0.5 + ... all other paths? 

The network is undirected, g is an adjacency matrix, with 250 nodes. 

This is the command I used: 

katz0.5 <- alpha.centrality(g, nodes=V(g), alpha=0.5, loops=FALSE,

                            exo=0.5, weights=NA,tol=1e-7, sparse=TRUE)

Thanks for your help !