I have a 500x500 adjacency matrix of 1 and 0, and I need to calculate pagerank for each page. I have a code here, where R is the matrix and T=0.15 is a constant:
n = ncol(R)
B = matrix(1/n, n, n) # the teleportation matrix
A = 0.85 * R + 0.15 * B
ranks = eigen(A)$vectors[1] # my PageRanks
print(ranks)
[1] -0.5317519+0i
I don't have much experience with R, but I assume that the given output is a general pagerank, and I need a pagerank for each page.
Is there a way to construct a table of pageranks with relation to the matrix? I didn't find anything related to my particular case in the web.
Few points:
(1) You need to convert the binary adjacency matrix (R in your case) to a column-stochastic transition matrix to start with (representing probability of transitions between the pages).
(2) A needs to remain as column stochastic as well, then only the dominant eigenvector corresponding to the eigenvalue 1 will be the page rank vector.
(3) To find the first eigenvector of the matrix A, you need use eigen(A)$vectors[,1]
Example with a small 5x5 adjacency matrix R:
set.seed(12345)
R = matrix(sample(0:1, 25, replace=TRUE), nrow=5) # random binary adjacency matrix
R = t(t(R) / rowSums(t(R))) # convert the adjacency matrix R to a column-stochastic transition matrix
n = ncol(R)
B = matrix(1/n, n, n) # the teleportation matrix
A = 0.85 * R + 0.15 * B
A <- t(t(A) / rowSums(t(A))) # make A column-stochastic
ranks = eigen(A)$vectors[,1] # my PageRanks
print(ranks)
# [1] 0.05564937 0.05564937 0.95364105 0.14304616 0.25280990
print(ranks / sum(ranks)) # normalized ranks
[1] 0.03809524 0.03809524 0.65282295 0.09792344 0.17306313