DirectedClustering (version 1.0.0)

ClustF: Clustering Coefficients for Directed/Undirected and Weighted Networks

Description

This function computes both Local and Global (average) Clustering Coefficients for either Directed/Undirected and Unweighted/Weighted Networks. The formulas are based on Onnela et al. (2005) for undirected networks, and on Fagiolo (2007) for directed networks.

Usage

ClustF(mat, type = "undirected", isolates = "zero", norm = 1)

Value

A list with the following components:

LocalCC

Local clustering coefficients for undirected networks

GlobalCC

Global clustering coefficient for undirected networks

cycleCC

Local Cycle clustering coefficients for directed networks

middlemanCC

Local Middleman clustering coefficients for directed networks

inCC

Local In clustering coefficients for directed networks

outCC

Local Out clustering coefficients for directed networks

totalCC

Local Total clustering coefficients for directed networks

GlobalcycleCC

Global Cycle clustering coefficient for directed networks

GlobalmiddlemanCC

Global Middleman clustering coefficient for directed networks

GlobalinCC

Global In clustering coefficient for directed networks

GlobaloutCC

Global Out clustering coefficient for directed networks

GlobaltotalCC

Global Total clustering coefficient for directed networks

Arguments

mat

A weighted adjacency matrix. If weights are greater than one, a normalization is provided by dividing each weight by the maximum weight observed.

type

The type of clustering coefficient to calculate. Possible values are: "undirected" (default) or "directed".

isolates

Character scalar, defines how to treat vertices with degree zero and one. If "NaN", their local transitivity is reported as NaN and they are not included in the averaging. If "zero", their transitivity is reported as 0 and they are included in the averaging. Default is "zero".

norm

If it is 1 (default), the link's weights are normalized by dividing by the maximum observed weight (as proposed by Fagiolo). If it is 0, weights are not normalized. Weights are always normalized when the maximum weight is greater than zero, ensuring that the clustering coefficient ranges between 0 and 1.

Author

Gian Paolo Clemente,

Details

In the directed case, different components of the directed clustering coefficient are also considered.

The function computes Onnela et al.'s (2005) formula for weighted and undirected networks. For directed networks, Fagiolo's (2007) formula is used. In the case of unweighted and undirected graphs, the classical local clustering coefficient (Watts and Strogatz) is provided. Local coefficients are computed for each node, and the global coefficient is the average of these local coefficients. These coefficients do not work for graphs with multiple or loop edges, so loops are removed.

References

Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76(2).

Onnela, J.P., Saramaki, J., Kertsz, J., & Kaski, K. (2005). Intensity and coherence of motifs in weighted complex networks. Physical Review E, 71(6).

Watts, D.J., & Strogatz, S.H. (1998). Collective dynamics of 'small-world' networks. Nature, 393, 440-442.

Examples

if (requireNamespace("igraph", quietly = TRUE)) {
  library(igraph)
  # Generate a weighted and undirected graph
  gsim <- sample_gnp(50, 0.5, directed = FALSE, loops = FALSE)
  PESI <- runif(length(E(gsim)), 0, 1)
  E(gsim)$weight <- PESI
  A <- as_adjacency_matrix(gsim, sparse = FALSE, attr = "weight")
  OnnelaClust <- ClustF(A, "undirected")

  # Generate a weighted and directed graph
  gsim <- sample_gnp(50, 0.5, directed = TRUE, loops = FALSE)
  PESI <- runif(length(E(gsim)), 0, 1)
  E(gsim)$weight <- PESI
  A <- as_adjacency_matrix(gsim, sparse = FALSE, attr = "weight")
  FagioloClust <- ClustF(A, "directed")
} else {
  cat("Please install the 'igraph' package to run this example.\n")
}