LinkRankMod: LinkRank Modularity

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

LinkRank Modularity

Description

Computes the LinkRank Modularity (Qlr), as described by Kim et al. [1]

Usage

LinkRankMod(L, pr, c)

Arguments

L	LinkRank Matrix. Output of LinkRank function
pr	PageRank vector. Output of pageRank function
c	partition vector

Details

The LinkRank Modularity (Qlr) is a modified modularity for both directed and undirected networks, defined as [1]

Qlr = (fraction of time spent walking within communities by a random walker) - (expected value of this fraction).

According to this definition, "a community is no longer a group of nodes in which links are more densely located. Instead, a community is a group of nodes in which a random walker is more likely to stay" [1].

Value

LinkRank Modularity value

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
L <- LinkRank(G,pr)

# Assign a partition vector
c <- 1:100

# Calculate LinkRank Modularity
LinkRankMod(L,pr,c)

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