clustcoef_auto {qgraph}

Local clustering coefficients.

Description

Compute local clustering coefficients, both signed and unsigned and both for weighted and for unweighted networks.

Usage

clustcoef_auto(x, thresholdWS = 0, thresholdON = 0)
clustWS(x, thresholdWS=0)
clustZhang(x)
clustOnnela(x, thresholdON=0)

Arguments

x

An undirected graph. Can be a qgraph object, an igraph object, an adjacency matrix, a weight matrix and an edgelist, or a weighted edgelist.

thresholdWS

The threshold used to binarize a weighted network x to compute the binary clustering coefficients clustWS and signed_clustWS. Edges with weights lower than thresholdWS in absolute value are zeroed. For unweighted networks, thresholdWS = 0 is the suggested value.

thresholdON

In the computation of Onnela's clustering coefficient clustOnnela, edge of weights lower than thresholdON in absolute value are excluded. The value thresholdON = 0 (i.e., no edge is excluded) is generally suggested also for weighted networks.

Details

clustWS computes the clustering coefficient for unweighted networks introduced by Watts & Strogatz (1998) and the corresponding signed version (Costantini & Perugini, in press). ClustZhang computes the clustering coefficient for weighted networks introduced by Zhang & Horvath (2005) and the corresponding signed version (Costantini & Perugini, in press). clustOnnela computes the clustering coefficient for weighted networks introduced by Onnela et al. (2005) and the corresponding signed version (Costantini & Perugini, in press). clustering_auto automatically recognizes the kind of the input network x (weighted vs. unweighted, signed vs. unsigned) and computes a subset of indices according to the kind of the network: signed indices are not computed for unsigned networks and weighted indices are not computed for unweighted networks. However the unsigned indices are computed for signed networks, by considering the absolute value of the weights, and the unweighted indices are computed for weighted networks, after a binarization according to the parameter thresholdWS. clustering_auto computes also the weighted clustering coefficient by Barrat et al. (2004), relying on function transitivity from package igraph. For the computation of the local clustering coefficient, a node must have at least two neighbors: for nodes with less than two neighbors NaN is returned.

Value

A dataframe that includes one or more of the following indices.

clustWS

The Watts & Strogatz's (1998) unweighted clustering coefficient

signed_clustWS

The signed version of the Watts & Strogatz's clustering coefficient

clustZhang

The Zhang & Horvath's (2005) weighted clustering coefficient

signed_clustZhang

The signed version of the Zhang & Horvath's (2005) clustering coefficient

clustOnnela

The Onnela et al.'s (2005) clustering coefficient

signed_clustOnnela

The signed version of the Onnela et al.'s (2005) clustering coefficient

clustBarrat

The Barrat et al.'s (2004) weighted clustering coefficient

Warning

The function requires an undirected network. To convert a directed network to undirected use for instance function upper.tri (see examples).

Note

Part of the code has been adapted from package WGCNA (Langfelder & Horvath, 2008).

Author(s)

Giulio Costantini ([e-mail]), Sacha Epskamp ([e-mail])

References

Barrat, A., Barthelemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. In Proc. Natl. Acad. Sci. USA 101 (pp. 3747-3752).

Costantini, G., Perugini, M. (in press), Generalization of Clustering Coefficients to Signed Correlation Networks

Langfelder, P., & Horvath, S. (2008). WGCNA: an R package for weighted correlation network analysis. BMC Bioinformatics, 9, 559.

Onnela, J. P., Saramaki, J., Kertesz, J., & Kaski, K. (2005). Intensity and coherence of motifs in weighted complex networks. Physical Review E, 71(6), 065103.

Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of "small-world" networks. Nature, 393(6684), 440-442.

Zhang, B., & Horvath, S. (2005). A general framework for weighted gene co-expression network analysis. Statistical Applications in Genetics and Molecular Biology, 4(1).

See Also

centrality_auto

Examples

set.seed(1)
# generate a random (directed) network:
net_ig <- igraph::erdos.renyi.game(n=8, p.or.m=.4, type="gnp", directed=TRUE) 

# convert it to an adjacency matrix:
net <- as.matrix(igraph:::get.adjacency(net_ig, type="both")) 

# convert it to a signed and weighted network:
net <- net*matrix(rnorm(ncol(net)^2), ncol=ncol(net)) 

# make it undirected:
net[upper.tri(net)] <- t(net)[upper.tri(net)] 
clustcoef_auto(net)