# R Code for A Justification and Application of Eigenvector Centrality

**Econometric Sense**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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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 matrix A <- 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 eigenvectors max(EV$values) # find the maximum eigenvalue # get the eigenvector associated with the largest eigenvalue centrality <- data.frame(EV$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 M M <- 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^2 MM(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 -> infinity library(matrixcalc) # k = 5 ck(5)/frobenius.norm(ck(5)) # k = 10 ck(10)/frobenius.norm(ck(10)) print(v0) # k = 100 ck(100)/frobenius.norm(ck(100))

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**Econometric Sense**.

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