PageRank centrality

PageRank of Brin and Page (1998): the probability that a random walker, who follows the ties and sometimes jumps to a random node, is found in each node.

Usage

page_rank_centrality(
  A,
  damping = 0.85,
  digraph = TRUE,
  weighted = FALSE,
  tol = 1e-10,
  max_iter = 1000
)

Arguments

A

A square matrix

damping

Probability of following a tie instead of jumping to a random node

digraph

Whether the matrix is directed or undirected

weighted

Whether the matrix is weighted

tol

Tolerance of the power iteration

max_iter

Maximum number of iterations

Value

This function returns the PageRank of the nodes, which adds up to one.

Details

At each step, the walker follows one of the outgoing ties of the node with probability damping, and jumps to a node chosen at random with probability 1 - damping. The nodes without outgoing ties are treated as if they were connected to every node.

References

Brin, S. and Page, L. (1998). The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems, 30(1-7), 107–117. doi:10.1016/S0169-7552(98)00110-X

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 0, 0, 0,
  1, 0, 0, 0, 1,
  1, 0, 0, 0, 0,
  0, 0, 1, 0, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

page_rank_centrality(A, digraph = FALSE)
#>         a         b         c         d         e 
#> 0.3575578 0.1313080 0.2454920 0.1313080 0.1343341