embedding {econetwork}

Graph embeddings for comparing trophic network architectures

Description

Computation of different embeddings from a list of directed graphs

Usage

embedding(gList, method="metric2vec", groups=NULL)

Arguments

gList

A list of directed graph objects of class igraph. An edge must go from the predator to the prey.

method

Embedding method. This should be (an unambiguous abbreviation of) one of "metric2vec", "motif2vec", "group2vec" or "shortestpath2vec".

groups

A named vector of class character or integer indicating the group to which each node belongs to. The length of groups must correspond to the number of different nodes present in gList. The names names(groups) must correspond to the nodes names in gList. If NULL, the groups are not considered.

Details

This function computes a graph embedding from a list of graph.

Comparing the architecture of interaction networks in space or time is essential for understanding the assembly, trajectory, functioning and persistence of species communities. Graph embedding methods, which position networks into a vector space where nearby networks have similar architectures, could be ideal tools for this purposes.

Here, the proposed embedding methods are:

-"metric2vec": each column is a network metric. connectance: network connectance, modularity: network modularity (undirected graph), rangeTL: trophic level range, (trophic level is computed as in Williams & Martinez, 2004), meanTL: mean trophic level, SWTL: shortest weighted trophic level, meanOmni: mean level of omnivory (standard deviation of the trophic levels of the prey), propOmni: proportion of omnivorous species, propCanib: proportion of cannibal species, meanNbPrey: mean number of prey, sdNbPrey: standard deviation of the number of prey, skewNbPrey: skewness of the number of prey, meanNbPred: mean number of predators, sdNbPred: standard deviation of the number of predators, skewNbPred: skewness of the number of predators, propBasal: proportion of basal species (which have no prey), propTop: proportion of top species (which have no predator), propInter: proportion of intermediate species (which have prey and predator), sdVulnerability: standard deviation of the vulnerability (i.e. in-degree), sdGeneralism: standard deviation of the generalism (i.e. out-degree), transitivity: network transitivity, diameter: network diameter, meanSP: mean shortest path, assortativity: network assortativity.

-"motif2vec": Graph motifs are small connected subgraphs with a well-defined structure. Each column is the proportion of each of the 13 connected motifs as enumerated by the 'motifs' function.

-"group2vec": Groups proportion, where the groups are defined previously (e.g. taxonmic groups).

-"shortestpath2vec": Computing the proportion of shortest path lengths. Can use the groups as well, path length proportion is decomposed per source and target group in this case.

Value

embedding returns an object of class matrix where rows corresponds to the differents graphs and columns to the different dimensions in the embedding space.

Author(s)

Authors: Christophe Botella, Stephane Dray, Catherine Matias, Vincent Miele, Wilfried Thuiller

Maintainer: Vincent Miele <[e-mail]>

References

Christophe Botella, Stephane Dray, Catherine Matias, Vincent Miele & Wilfried Thuiller, An appraisal of graph embeddings for comparing trophic network architectures. Methods in Ecology and evolution (2021) <doi:10.1111/2041-210X.13738>

Williams, Richard J., and Neo D. Martinez. "Limits to trophic levels and omnivory in complex food webs: theory and data." The American Naturalist 163.3 (2004)

Examples

library(igraph)
# Generating a set of graphs with 3 groups
groups = rep(-1,60)
groups[1:20] = 1
groups[21:40] = 2
groups[41:60] = 3
names(groups) = as.character(1:60)

# A first set with a few links between groups 1 and 3
gList = c()
for(i in 1:5){
    pm <- rbind( c(0, .5, 0.05), c(0, 0, 0.5), c(0,0,0) )
    graphLoc <- sample_sbm(60, pref.matrix=pm, block.sizes=c(20,20,20), directed=TRUE)
    V(graphLoc)$name = as.character(1:60)
    gList = c(gList,list(graphLoc))
}
# A second set with many links between groups 1 and 3
for(i in (6:10)){
    pm <- rbind( c(0, .5, .5), c(0, 0, 0.5), c(0,0,0) )
    graphLoc <- sample_sbm(60, pref.matrix=pm, block.sizes=c(20,20,20), directed=TRUE)
    V(graphLoc)$name = as.character(1:60)
    gList = c(gList,list(graphLoc))
}
names(gList) = LETTERS[1:10]

# Computing different embeddings and
usermfrow <- par()$mfrow
par(mfrow=c(2,2))

embd <- embedding(gList, method="metric2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="metric2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList,  method="motif2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="motif2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList, method="shortestpath2vec")
pca <- prcomp(embd, rank=2)$x
plot(pca, main="shortestpath2vec")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

embd <- embedding(gList, method="shortestpath2vec", groups)
pca <- prcomp(embd, rank=2)$x
plot(pca, main="shortestpath2vec_group")
text(x=pca[,1], y=pca[,2], labels=rownames(embd), pos=2, col=c(rep("blue",5),rep("red",5)))

par(mfrow=usermfrow)