ClustBCG: Clustering Coefficient for Directed/Undirected and Weighted Networks (Barrat et al. (2004) and Clemente, Grassi (2018) coefficients).

Description

Compute Local and Global (average) Clustering Coefficients for Directed/Undirected and Unweighted/Weighted Networks. Formulas are based on Barrat et al. (2004) coefficient when the network is undirected, while it is based on Clemente and Grassi (2018) proposal when the network is directed. In the directed case, different components of directed clustering coefficient are also provided.

Usage

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

Arguments

mat

A Weighted Adjacency Matrix

type

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

isolates

Character scalar, defines how to treat vertices with degree zero and one. If it is 'NaN' then their local transitivity is reported as NaN and they are not included in the averaging. If it is 'zero', then we report 0 transitivity for them, and they are included in the averaging. Default value is 'zero'.

Value

For 'undirected case':

LocalCC

Local clustering coefficients

GlobalCC

Global clustering coefficient

For 'directed case':

cycleCC

Local Cycle clustering coefficients

middlemanCC

Local Middleman clustering coefficients

inCC

Local In clustering coefficients

outCC

Local Out clustering coefficients

totalCC

Local Total clustering coefficients

GlobalcycleCC

Global Cycle clustering coefficient

GlobalmiddlemanCC

Global Middleman clustering coefficient

GlobalinCC

Global In clustering coefficient

GlobaloutCC

Global Out clustering coefficient

GlobaltotalCC

Global Total clustering coefficient

Details

The function ClustBCG computes Barrat et al. coefficient when a weighted and undirected network is considered. For directed network Clemente and Grassi formula is computed. In case of unweighted and undirected graphs, it provides classical local clustering coefficient (Watts and Strogatz).

In all cases, local clustering coefficients are obtained for each node, the global coefficient is the average of local coefficients. These clustering coefficients do not work for graphs with multiple and/or loop edges. Hence, loops are removed. In the directed case, different components of directed clustering coefficient are also considered.

References

Barrat, A. and Barthelemy, M. and Pastor-Satorras, R. and Vespignani, A. (2004) The architecture of complex weighted networks, Proc. Natl. Acad. Sci., USA 101, 3747.

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

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

Examples

Run this code

# NOT RUN {
library(igraph)
#Generate a Weighted and Undirected graph with Erdos Renyi Model
gsim<-erdos.renyi.game(50, 0.5, type="gnp", directed = FALSE, loops = FALSE)
PESI<-runif(length(E(gsim)), 0, 1)
E(gsim)$weight<-PESI

#Get Adjacency
A<-get.adjacency(gsim, sparse=FALSE, attr="weight")
#Compute Barrat et al. (2004) coefficient
BarratClust<-ClustBCG(A, "undirected")

#The same results can be obtained with igraph::transitivity
check<-sum(BarratClust$LocalCC-transitivity(gsim, "weighted"))

#Generate a Weighted and Directed Graph with Erdos Renyi Model
gsim<-erdos.renyi.game(50, 0.5, type="gnp", directed = TRUE, loops = FALSE)
PESI<-runif(length(E(gsim)), 0, 1)
E(gsim)$weight<-PESI

#Get Adjacency
A<-get.adjacency(gsim, sparse=FALSE, attr="weight")

#Compute Clemente, Grassi (2018) coefficient
CGClust<-ClustBCG(A, "directed")
# }

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