LinkRank: LinkRank Matrix

In leb-fmvz-usp/epinemo: An R Package for EPIdemiological NEtwork MOdels

LinkRank Matrix

Description

Calculates the LinkRank Matrix, according to Kim et al. [1].

Usage

LinkRank(G, pr)

Arguments

G	Google Matrix. Output of GoogleMatrix function
pr	PageRank vector. Output of pageRank function

Details

"Similar to the definition of PageRank, LinkRank of a particular link should be equal to the probability that a random walker follows the link from node i to node j" [1]. LinkRank from node i to node j can be defined as L_{ij} = π_{i} * G_{ij}, where π_{i} is the ith element of the PageRank vector, and G_{ij} is the element of the Google Matrix.

Value

LinkRank Matrix

References

[1] Kim Y, Son SW, Jeong H (2010). "Finding Communities in Directed Networks." Physical Review E 81, 016103. doi: 10.1103/PhysRevE.81.016103

Examples

# Generate an arbitrary 100 by 100 adjacency matrix with zeros and ones
# Remove loops
A <- matrix(rbinom(100 * 100, 1, 0.2), ncol = 100, nrow = 100)
diag(A) <- 0

# Calculate Google Matrix
G <- GoogleMatrix(A)

# Calculate PageRank vector
pr <- pageRank(A)

# Calculate LinkRank Matrix
LinkRank(G,pr)

leb-fmvz-usp/epinemo documentation built on Nov. 27, 2022, 10:58 p.m.