Hi all,
I have a question about the using the power-centrality function for computation of Bonacich centrality. I would like to construct a scaled power centrality with two 2 inputs, alpha and beta
From the power-centrality function, I can set the value of beta. In my case, I would like to set it to 3/4 of the reciprocal of the maximum eigenvalue of the network. (exponent=0.75/max_eigen)
However, there is a restriction to choose the scaling parameter alpha
The rescale option, if true, centrality scores are rescaled such that they sum to 1. I would like to choose the value of alpha such that the minimum centrality of a vertex is always equal to 1. Is there a solution to this issue?
Thank you for your help.

Code example:

  mynetwork= graph.data.frame(mydata,directed=FALSE)
  ec <- evcent(mynetwork)
  ec <- ec$vector  # evcent give the unnormalized eigenvector
  ed <- eigen(as.matrix(get.adjacency(mynetwork)))  # eigen return a normalized vector 
  ec2 <- ed$vectors[,1]
  max_eigen <- max(ec2)
 bonacich    <- power_centrality(network,
                               loops = FALSE, exponent=0.75/max_eigen, 
                               rescale = FALSE,
                               sparse = TRUE)