ClustBCG: Clustering Coefficient for Directed/Undirected and Weighted...

In GianPaoloClemente/DirectedClustering: Directed Weighted Clustering Coefficient

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")

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".

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.

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

Author(s)

Gian Paolo Clemente, [e-mail]

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")
}

GianPaoloClemente/DirectedClustering documentation built on Sept. 25, 2024, 12:57 a.m.