DirectedClustering (version 1.0.0)

ClustBCG: Clustering Coefficient for Directed/Undirected and Weighted Networks

Description

Compute Local and Global (average) Clustering Coefficients for Directed/Undirected and Unweighted/Weighted Networks.

Usage

ClustBCG(mat, type = "undirected", isolates = "zero")

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.

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".

Author

Gian Paolo Clemente,

Details

Formulas are based on Barrat et al. (2004) for undirected networks, and on Clemente and Grassi (2018) for directed networks.

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

The function computes the Barrat et al. (2004) coefficient for a weighted and undirected network. For a directed network, the Clemente and Grassi (2018) formula is used. In case of unweighted and undirected graphs, the classical local clustering coefficient (Watts and Strogatz) is provided. Local clustering 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, hence loops are removed.

References

Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, USA, 101, 3747.

Clemente, G.P., & Grassi, R. (2018). Directed clustering in weighted networks: a new perspective. Chaos, Solitons and Fractals, 107, 26–38.

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)$weight <- PESI
  A <- as_adjacency_matrix(gsim, sparse = FALSE, attr = "weight")
  BarratClust <- ClustBCG(A, "undirected")
  check <- sum(BarratClust$LocalCC - transitivity(gsim, "weighted"))

  # 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")
  CGClust <- ClustBCG(A, "directed")
} else {
  cat("Please install the 'igraph' package to run this example.\n")
}