,
Rosanna Grassi [ctb]| Title: | Directed Weighted Clustering Coefficient |
|---|---|
| Description: | Allows the computation of clustering coefficients for directed and weighted networks by using different approaches. It allows to compute clustering coefficients that are not present in 'igraph' package. A description of clustering coefficients can be found in "Directed clustering in weighted networks: a new perspective", Clemente, G.P., Grassi, R. (2017), <doi:10.1016/j.chaos.2017.12.007>. |
| Authors: | Gian Paolo Clemente [cre, aut]
,
Rosanna Grassi [ctb] |
| Maintainer: | Gian Paolo Clemente <[email protected]> |
| License: | GPL-3 | file LICENSE |
| Version: | 1.0.0 |
| Built: | 2025-02-21 05:15:03 UTC |
| Source: | https://github.com/gianpaoloclemente/directedclustering |
The DirectedClustering R package presented here includes an enhanced R implementation of Local and Global (average) Clustering Coefficients for Directed/Undirected and Unweighted/Weighted Networks.
Functions are based on Barrat et al. (2004) and Onnela et al. (2005) coefficients when the network is undirected, while it is based on Fagiolo (2007) and Clemente and Grassi (2018) proposals when the network is directed. In the directed case, different components of directed clustering coefficient are also considered.
Details of alternative coefficients computed by DirectedClustering R package can be found in Clemente, Grassi (2018).
Please report any issue arising or bug in the code to [email protected].
This package and the functions herein are provided as is, without any guarantee regarding the accuracy of calculations. The authors disclaim any liability arising by any losses due to direct and indirect use of this package.
Gian Paolo Clemente, [email protected], Rosanna Grassi, [email protected]
Clemente, G.P. and Grassi, R. (2018) Directed clustering in weighted networks: a new perspective, Chaos, Solitons and Fractals, 107,26–38.
Compute Local and Global (average) Clustering Coefficients for Directed/Undirected and Unweighted/Weighted Networks.
ClustBCG(mat, type = "undirected", isolates = "zero")ClustBCG(mat, type = "undirected", isolates = "zero")
mat |
A weighted adjacency matrix. |
type |
The type of clustering coefficient to calculate.
Possible values are: |
isolates |
Character scalar, defines how to treat vertices with degree zero and one.
If |
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.
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 |
Gian Paolo Clemente, [email protected]
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.
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)$weight <- PESI A <- as_adjacency_matrix(gsim, sparse = FALSE, attr = "weight") CGClust <- ClustBCG(A, "directed") } else { cat("Please install the 'igraph' package to run this example.\n") }if (requireNamespace("igraph", quietly = TRUE)) { library(igraph) # Generate a weighted and undirected graph gsim <- sample_gnp(50, 0.5, directed = FALSE, loops = FALSE) PESI <- runif(length(E(gsim)), 0, 1) E(gsim)$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") }
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.
ClustF(mat, type = "undirected", isolates = "zero", norm = 1)ClustF(mat, type = "undirected", isolates = "zero", norm = 1)
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: |
isolates |
Character scalar, defines how to treat vertices with degree zero and one.
If |
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. |
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.
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 |
Gian Paolo Clemente, [email protected]
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.
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") }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") }