DirectedClustering (version 0.1.1)

ClustF: Clustering Coefficients for Directed/Undirected and Weighted Networks (Onnela et al. (2005) and Fagiolo (2007) coefficients)

Description

This function computes both Local and Global (average) Clustering Coefficients for either Directed/Undirected and Unweighted/Weighted Networks.
Formulas are based on Onnela et al. (2005) coefficient when the network is undirected, while it is based on Fagiolo (2007) coefficient when the network is directed.
In the directed case, different components of directed clustering coefficient are also considered.

Usage

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

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

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 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'.

norm

If it is 1 (default), link's weights are normalized by dividing by the maximum observed weight (as proposed in Fagiolo). Otherwise, weights are not normalized. It is worth pointing out that weights are always normalized when the maximum weight is greater than zero. This normalization assures that clustering coefficient ranges between 0 and 1.

Author

Gian Paolo Clemente, [e-mail]

Details

The function ClustF computes Onnela et al. formula when weighted and undirected networks are considered.
For directed networks, Fagiolo formula is computed. In case of unweighted and undirected graphs, it provides classical local clustering coefficient (Watts and Strogatz).

Local 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 provided.

References

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

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

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

Examples

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 Onnela et al. (2005) coefficient
OnnelaClust<-ClustF(A, "undirected")

#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 Fagiolo (2007) coefficient
FagioloClust<-ClustF(A, "directed")