# R Code for A Justification and Application of Eigenvector Centrality

November 8, 2012
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Leo Spizzirri  does an excellent job of providing mathematical intuition behind eigenvector centrality. As I was reading through it, I found it easier to just work through the matrix operations he proposes using R.  You can find his paper here: https://www.math.washington.edu/~morrow/336_11/papers/leo.pdf

My R code follows. This is for the example using degree centrality which made the most sense to me. For some reason, in the last section, for very large k there is an issue with computing the vector, I think it is stemming from my definition of B_K. The same issue occurs with large k using the function MM. It could be that the values get too large for R to handle?  Regardless, as pointed out on page 7, even at  k = 10 that ck approaches the eigenvector.

`# *------------------------------------------------------------------# | PROGRAM NAME: R_BASIC_SNA# | DATE: 4/9/12# | CREATED BY: MATT BOGARD# | DATE: 11/5/12 # | PROJECT FILE: P:\R  Code References\SNA            # *----------------------------------------------------------------# | PURPOSE: COMPANION CODE TO Justification and Application of# |  Eigenvector Centrality by Leo Spizzirri        # |  https://www.math.washington.edu/~morrow/336_11/papers/leo.pdf# *------------------------------------------------------------------  # specify the adjacency matrixA <- matrix(c(0,1,0,0,0,0,                        1,0,1,0,0,0,                        0,1,0,1,1,1,                        0,0,1,0,1,0,                        0,0,1,1,0,1,                        0,0,1,0,1,0 ),6,6, byrow= TRUE)EV <- eigen(A) # compute eigenvalues and eigenvectorsmax(EV\$values)  # find the maximum eigenvalue # get the eigenvector associated with the largest eigenvaluecentrality <- data.frame(EV\$vectors[,1]) names(centrality) <- "Centrality"print(centrality) B <- A + diag(6)EVB <- eigen(B) # compute eigenvalues and eigenvectors         # they are the same as EV(A) # define matrix MM <- matrix(c(1,1,0,0,                        1,1,1,0,                        0,1,1,1,                        0,0,1,1),4,4, byrow= TRUE) # define function for B^k for matrix M      MM <- function(k){                  n <- (k-1)     B_K <- C           for (i in 1:n){    B_K <- B_K%*%M     }     return(B_K)} MM(2) # M^2MM(3) # M^3 # define c c <- matrix(c(2,3,5,3,4,3)) # define c_k for matrix B ck <- function(k){                  n <- (k-2)     B_K <- B           for (i in 1:n){    B_K <- B_K%*%B     }    c_k <- B_K%*%c       return(c_k)} # derive EV centrality as k -> infinitylibrary(matrixcalc)# k  = 5ck(5)/frobenius.norm(ck(5))# k  = 10ck(10)/frobenius.norm(ck(10))print(v0)# k = 100ck(100)/frobenius.norm(ck(100))`

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