R/graphVARX1.r
In wvanwie/ragt2ridges: Ridge Estimation of Vector Auto-Regressive (VAR) Processes
Defines functions
graphVARX1
Documented in
graphVARX1
graphVARX1 <- function(sparseA,
sparseB,
sparseP,
type="TSCG",
side="right",
prune=TRUE,
nNamesY=NULL,
nNamesX=NULL,
main=NULL,
vertex.color.X="lightcyan2",
vertex.color.T0="lightcyan2",
vertex.color.T1="lightcyan2",
vertex.frame.color="steelblue",
vertex.label.cex=-1,
vertex.label.color.X="black",
vertex.label.color.T0="black",
vertex.label.color.T1="black",
vertex.label.font=1.5,
vertex.size=-1,
edge.arrow.size=-1,
edge.width=-1,
...){
#######################################################################
#
# DESCRIPTION:
# Plot temporal relations as implied by A and B (the matrices with lag
# one and two regression coefficient of the VAR(2)) model.
#
# ARGUMENTS:
#
# -> sparseA : Matrix A1 of lag one regression
# parameters, which is assumed to be sparse.
# -> sparseB : Matrix A2 of lag two regression
# parameters, which is assumed to be sparse.
# -> sparseP : Matrix P of precision of the error, which
# is assumed to be sparse.
# -> type : A 'character' indicating what should be
# plotted. If type='TSCG'. the time series
# chain graph is plotted, while type
# type='Aonly' limits this graph
# to the temporal relations. If
# type='globalPC' or type='contempPC', the
# global or contemporaneous (respectively)
# partial correlation graph is plotted.
# -> side : A 'character' indicating wether the
# contemporaneous dependencies should be
# plotted on the 'left' (time t) or the
# 'right' (time t+1) side. Only active
# when type='TSCG'.
# -> prune : A 'logical' indicating whether to remove
# covariates without any temporal relations
# (as implied by 'sparseA', 'sparseB',
# 'sparseP').
# -> nNamesY : A 'character' containing the Y variate
# names to written inside the nodes.
# -> nNamesX : A 'character' containing the X covariate
# names to written inside the nodes.
# -> main : The 'character' to be plotted as title
# above the graph.
# -> vertex.color.X : Color of nodes at time point t.
# -> vertex.color.T0 : Color of nodes at time point t+1. Ignored
# when type='globalPC' or type='contempPC'.
# -> vertex.color.T1 : Color of nodes at time point t+2. Ignored
# when type='globalPC' or type='contempPC'.
# -> vertex.frame.color : Refer to 'plot.igraph'.
# -> vertex.label.cex : Refer to 'plot.igraph'.
# -> vertex.label.color.X : Color of the node label at time point t.
# -> vertex.label.color.T0 : Color of the node label at time point t+1.
# Ignored when type='globalPC' or
# type='contempPC'.
# -> vertex.label.color.T1 : Color of the node label at time point t+2.
# Ignored when type='globalPC' or
# type='contempPC'.
# -> vertex.label.font : Refer to 'plot.igraph'.
# -> vertex.size : Refer to 'plot.igraph'.
# -> edge.arrow.size : Refer to 'plot.igraph'.
# -> edge.width : Refer to 'plot.igraph'.
# -> ... : Other arguments to be passed to
# 'plot.igraph'.
#
# DEPENDENCIES:
# library(igraph) # functions: delete.edges, E, ecount,
# plot.igraph, graph.adjacency,
# maximum.cardinality.search
#
# NOTES:
# - igraph does not support visualization of mixed graphs, including both
# directed and undirected edges. As a consequence the time-series chain
# graph is undirected: the edges from t to t+1 should be thought of
# as directed.
# - if "white" labels, color combination "navy" and "blue" looks nice.
# - if "black" labels, color combination "tomato1" and "red" looks nice.
#
#######################################################################
# input check
if (as.character(class(sparseA)) != "matrix"){
stop("Input (sparseA) is of wrong class.")
}
if (nrow(sparseA) != ncol(sparseA)){
stop("Matrix sparseA is not square.")
}
if (as.character(class(sparseB)) != "matrix"){
stop("Input (sparseB) is of wrong class.")
}
if (nrow(sparseB) != ncol(sparseA)){
stop("Number of rows of matrix sparseB does not match with that of sparseA.")
}
if (as.character(class(sparseP)) != "matrix"){
stop("Input (sparseP) is of wrong class.")
}
if (nrow(sparseP) != ncol(sparseP)){
stop("Matrix sparseP is not square.")
}
if (as.character(class(prune)) != "logical"){
stop("Input (prune) is of wrong class.")
}
if (as.character(class(vertex.size)) != "numeric"){
stop("Input (vertex.size) is of wrong class.")
}
if (as.character(class(vertex.color.X)) != "character"){
stop("Input (vertex.color.X) is of wrong class.")
}
if (as.character(class(vertex.color.T0)) != "character"){
stop("Input (vertex.color.T0) is of wrong class.")
}
if (as.character(class(vertex.label.color.X)) != "character"){
stop("Input (vertex.label.color.X) is of wrong class.")
}
if (as.character(class(vertex.label.color.T0)) != "character"){
stop("Input (vertex.label.color.T0) is of wrong class.")
}
# if no covariate names are specified the columns and
# row names of A and B and P are given names 1, 2, et cetera
if (is.null(nNamesY)){
nNamesY <- as.character(1:nrow(sparseA))
}
if (is.null(nNamesX)){
nNamesX <- as.character(1:ncol(sparseB))
}
if (type=="TSCG"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes of A and B
nNodesY <- nrow(sparseA)
nNodesX <- ncol(sparseB)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(6*(nrow(sparseA))^(-0.8), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseA))^(-0.7), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "VARX(1) time-series chain graph"
}
# specify plot layout
if (nrow(sparseA) %% 2 == 1){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2) +
1/2, length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2) + 1/2, nrow(sparseA) +
1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
if (nrow(sparseA) %% 2 == 0){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2),
length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2 + 1), nrow(sparseA) +
1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
# contempory independencies
contCIG <- sparseP
contCIG[sparseP != 0] <- 1
diag(contCIG) <- 0
contCIG[lower.tri(contCIG)] <- 0
if (side == "right"){
# size of the edges
edge.widthA <- abs(sparseA)[which(sparseA != 0, arr.ind=TRUE)]
edge.widthB <- abs(sparseB)[which(sparseB != 0, arr.ind=TRUE)]
edge.widthP <- abs(sparseP[which(contCIG != 0, arr.ind=TRUE)])
edge.widthA <- edge.widthA / max(edge.widthA)
edge.widthB <- edge.widthB / max(edge.widthB)
edge.widthP <- edge.widthP / max(edge.widthP)
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * c(edge.widthA, edge.widthB, edge.widthP)
} else {
edge.width <- edge.width * c(edge.widthA, edge.widthB, edge.widthP)
}
# create adjacency matrix
adjMat <- rbind(cbind(0*sparseA, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# arrow heads of curved edges should be zero width
curved <- rep(0, sum(adjMat))
curved[-c(1:sum(adjMat[1:(nNodesX + nNodesY),]))] <- -1
# specify negative edges
negEdgesA <- which(sparseA[which(sparseA != 0)] < 0)
negEdgesB <- length(which(sparseA != 0)) +
which(sparseB[which(sparseB != 0)] < 0)
negEdges <- c(negEdgesA, negEdgesB, length(which(sparseA != 0)) +
length(which(sparseB != 0)) +
which(sparseP[which(contCIG != 0, arr.ind=TRUE)] < 0))
# specify positive edges
posEdgesA <- which(sparseA[which(sparseA != 0)] > 0)
posEdgesB <- length(which(sparseA != 0)) +
which(sparseB[which(sparseB != 0)] > 0)
posEdges <- c(posEdgesA, posEdgesB, length(which(sparseA != 0)) +
length(which(sparseB != 0)) +
which(sparseP[which(contCIG != 0, arr.ind=TRUE)] > 0))
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font,
edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX),
rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.curved=curved,
edge.lty=igraph::E(gObj)$style, margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
if (side == "bottomleft"){
# create adjacency matrix
adjMat <- rbind(cbind(contCIG, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# width of the edges
Pslh <-sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
maxA <- max(abs(sparseA))
maxB <- max(abs(sparseB))
maxP <- max(abs(sparseP))
adjMatSlh <- rbind(cbind(Pslh/maxP, 0*sparseB, t(sparseA)/maxA),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)/maxB),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
# default node size and font size if not provided
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
} else {
edge.width <- edge.width * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
}
# arrow heads of curved edges should be zero width
curved <- rep(0, sum(adjMat))
slh <- which(adjMat[1, c(1:nrow(sparseP))]==1)
if (length(slh) > 0){ idCurved <- 1:length(slh) } else { idCurved <- numeric() }
for (j in 2:nrow(sparseP)){
slh <- which(adjMat[j, c(1:nrow(sparseP))]==1)
if (length(slh) > 0){
idCurved <- c(idCurved, 1:length(slh) + sum(adjMat[1:(j-1),]))
}
}
curved[idCurved] <- 1
# identify negative and positive edges
Pslh <-sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
adjMatSlh <- rbind(cbind(Pslh, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
diag(adjMatSlh) <- 0
edgeSigns <- sign(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
negEdges <- which(edgeSigns < 0)
posEdges <- which(edgeSigns > 0)
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font, edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX),
rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.curved=curved,
edge.lty=igraph::E(gObj)$style,
margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
}
if (type=="ABonly"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes of A and B
nNodesY <- nrow(sparseA)
nNodesX <- ncol(sparseB)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(6*(nrow(sparseA))^(-0.8), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseA))^(-0.7), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "Cross-time and covariate relations of VARX(1) model"
}
# specify plot layout
if (nrow(sparseA) %% 2 == 1){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2) + 1/2, length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2) + 1/2, nrow(sparseA) + 1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
if (nrow(sparseA) %% 2 == 0){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2), length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2 + 1), nrow(sparseA) + 1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
# create adjacency matrix
adjMat <- rbind(cbind(0*contCIG, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# width of the edges
Pslh <- 0 * sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
maxA <- max(abs(sparseA))
maxB <- max(abs(sparseB))
maxP <- max(abs(sparseP))
adjMatSlh <- rbind(cbind(Pslh/maxP, 0*sparseB, t(sparseA)/maxA),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)/maxB),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
# size of the edges
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
} else {
edge.width <- edge.width * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
}
# identify negative and positive edges
Pslh <- 0*sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
adjMatSlh <- rbind(cbind(0*Pslh, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
diag(adjMatSlh) <- 0
edgeSigns <- sign(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
negEdges <- which(edgeSigns < 0)
posEdges <- which(edgeSigns > 0)
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font, edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX), rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.lty=igraph::E(gObj)$style,
margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
if (type=="contempPC"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes
nNodes <- nrow(sparseP)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(8*(nrow(sparseP))^(-0.6), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseP))^(-0.6), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "Contemp. cond. independence graph of VARX(1) model"
}
# get global CIG
CIG <- CIGofVAR1(sparseA, sparseP, type="contemp")
diag(CIG) <- 0
gObj <- graph.adjacency(CIG, "undirected")
# size of the edges
if (edge.width <= 0){ edge.width <- 10 * (nrow(sparseP)^(-0.8)) }
if (edge.width > 0){ edge.width <- edge.width }
# actual plotting
plot.igraph(gObj,
layout=layout.circle,
vertex.size=rep(vertex.size, nNodes),
vertex.label.font=vertex.label.font,
vertex.color=rep(vertex.color.X, nNodes),
vertex.frame.color=vertex.frame.color,
edge.color="black",
vertex.label=nNamesY,
vertex.label.cex=vertex.label.cex,
vertex.label.color=rep(vertex.label.color.X, nNodes),
edge.width=edge.width,
vertex.label.family="sans",
main=main, ...)
}
}
wvanwie/ragt2ridges documentation built on May 4, 2019, 12:03 p.m.
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Defines functions graphVARX1
Documented in graphVARX1
graphVARX1 <- function(sparseA,
sparseB,
sparseP,
type="TSCG",
side="right",
prune=TRUE,
nNamesY=NULL,
nNamesX=NULL,
main=NULL,
vertex.color.X="lightcyan2",
vertex.color.T0="lightcyan2",
vertex.color.T1="lightcyan2",
vertex.frame.color="steelblue",
vertex.label.cex=-1,
vertex.label.color.X="black",
vertex.label.color.T0="black",
vertex.label.color.T1="black",
vertex.label.font=1.5,
vertex.size=-1,
edge.arrow.size=-1,
edge.width=-1,
...){
#######################################################################
#
# DESCRIPTION:
# Plot temporal relations as implied by A and B (the matrices with lag
# one and two regression coefficient of the VAR(2)) model.
#
# ARGUMENTS:
#
# -> sparseA : Matrix A1 of lag one regression
# parameters, which is assumed to be sparse.
# -> sparseB : Matrix A2 of lag two regression
# parameters, which is assumed to be sparse.
# -> sparseP : Matrix P of precision of the error, which
# is assumed to be sparse.
# -> type : A 'character' indicating what should be
# plotted. If type='TSCG'. the time series
# chain graph is plotted, while type
# type='Aonly' limits this graph
# to the temporal relations. If
# type='globalPC' or type='contempPC', the
# global or contemporaneous (respectively)
# partial correlation graph is plotted.
# -> side : A 'character' indicating wether the
# contemporaneous dependencies should be
# plotted on the 'left' (time t) or the
# 'right' (time t+1) side. Only active
# when type='TSCG'.
# -> prune : A 'logical' indicating whether to remove
# covariates without any temporal relations
# (as implied by 'sparseA', 'sparseB',
# 'sparseP').
# -> nNamesY : A 'character' containing the Y variate
# names to written inside the nodes.
# -> nNamesX : A 'character' containing the X covariate
# names to written inside the nodes.
# -> main : The 'character' to be plotted as title
# above the graph.
# -> vertex.color.X : Color of nodes at time point t.
# -> vertex.color.T0 : Color of nodes at time point t+1. Ignored
# when type='globalPC' or type='contempPC'.
# -> vertex.color.T1 : Color of nodes at time point t+2. Ignored
# when type='globalPC' or type='contempPC'.
# -> vertex.frame.color : Refer to 'plot.igraph'.
# -> vertex.label.cex : Refer to 'plot.igraph'.
# -> vertex.label.color.X : Color of the node label at time point t.
# -> vertex.label.color.T0 : Color of the node label at time point t+1.
# Ignored when type='globalPC' or
# type='contempPC'.
# -> vertex.label.color.T1 : Color of the node label at time point t+2.
# Ignored when type='globalPC' or
# type='contempPC'.
# -> vertex.label.font : Refer to 'plot.igraph'.
# -> vertex.size : Refer to 'plot.igraph'.
# -> edge.arrow.size : Refer to 'plot.igraph'.
# -> edge.width : Refer to 'plot.igraph'.
# -> ... : Other arguments to be passed to
# 'plot.igraph'.
#
# DEPENDENCIES:
# library(igraph) # functions: delete.edges, E, ecount,
# plot.igraph, graph.adjacency,
# maximum.cardinality.search
#
# NOTES:
# - igraph does not support visualization of mixed graphs, including both
# directed and undirected edges. As a consequence the time-series chain
# graph is undirected: the edges from t to t+1 should be thought of
# as directed.
# - if "white" labels, color combination "navy" and "blue" looks nice.
# - if "black" labels, color combination "tomato1" and "red" looks nice.
#
#######################################################################
# input check
if (as.character(class(sparseA)) != "matrix"){
stop("Input (sparseA) is of wrong class.")
}
if (nrow(sparseA) != ncol(sparseA)){
stop("Matrix sparseA is not square.")
}
if (as.character(class(sparseB)) != "matrix"){
stop("Input (sparseB) is of wrong class.")
}
if (nrow(sparseB) != ncol(sparseA)){
stop("Number of rows of matrix sparseB does not match with that of sparseA.")
}
if (as.character(class(sparseP)) != "matrix"){
stop("Input (sparseP) is of wrong class.")
}
if (nrow(sparseP) != ncol(sparseP)){
stop("Matrix sparseP is not square.")
}
if (as.character(class(prune)) != "logical"){
stop("Input (prune) is of wrong class.")
}
if (as.character(class(vertex.size)) != "numeric"){
stop("Input (vertex.size) is of wrong class.")
}
if (as.character(class(vertex.color.X)) != "character"){
stop("Input (vertex.color.X) is of wrong class.")
}
if (as.character(class(vertex.color.T0)) != "character"){
stop("Input (vertex.color.T0) is of wrong class.")
}
if (as.character(class(vertex.label.color.X)) != "character"){
stop("Input (vertex.label.color.X) is of wrong class.")
}
if (as.character(class(vertex.label.color.T0)) != "character"){
stop("Input (vertex.label.color.T0) is of wrong class.")
}
# if no covariate names are specified the columns and
# row names of A and B and P are given names 1, 2, et cetera
if (is.null(nNamesY)){
nNamesY <- as.character(1:nrow(sparseA))
}
if (is.null(nNamesX)){
nNamesX <- as.character(1:ncol(sparseB))
}
if (type=="TSCG"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes of A and B
nNodesY <- nrow(sparseA)
nNodesX <- ncol(sparseB)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(6*(nrow(sparseA))^(-0.8), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseA))^(-0.7), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "VARX(1) time-series chain graph"
}
# specify plot layout
if (nrow(sparseA) %% 2 == 1){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2) +
1/2, length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2) + 1/2, nrow(sparseA) +
1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
if (nrow(sparseA) %% 2 == 0){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2),
length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2 + 1), nrow(sparseA) +
1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
# contempory independencies
contCIG <- sparseP
contCIG[sparseP != 0] <- 1
diag(contCIG) <- 0
contCIG[lower.tri(contCIG)] <- 0
if (side == "right"){
# size of the edges
edge.widthA <- abs(sparseA)[which(sparseA != 0, arr.ind=TRUE)]
edge.widthB <- abs(sparseB)[which(sparseB != 0, arr.ind=TRUE)]
edge.widthP <- abs(sparseP[which(contCIG != 0, arr.ind=TRUE)])
edge.widthA <- edge.widthA / max(edge.widthA)
edge.widthB <- edge.widthB / max(edge.widthB)
edge.widthP <- edge.widthP / max(edge.widthP)
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * c(edge.widthA, edge.widthB, edge.widthP)
} else {
edge.width <- edge.width * c(edge.widthA, edge.widthB, edge.widthP)
}
# create adjacency matrix
adjMat <- rbind(cbind(0*sparseA, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# arrow heads of curved edges should be zero width
curved <- rep(0, sum(adjMat))
curved[-c(1:sum(adjMat[1:(nNodesX + nNodesY),]))] <- -1
# specify negative edges
negEdgesA <- which(sparseA[which(sparseA != 0)] < 0)
negEdgesB <- length(which(sparseA != 0)) +
which(sparseB[which(sparseB != 0)] < 0)
negEdges <- c(negEdgesA, negEdgesB, length(which(sparseA != 0)) +
length(which(sparseB != 0)) +
which(sparseP[which(contCIG != 0, arr.ind=TRUE)] < 0))
# specify positive edges
posEdgesA <- which(sparseA[which(sparseA != 0)] > 0)
posEdgesB <- length(which(sparseA != 0)) +
which(sparseB[which(sparseB != 0)] > 0)
posEdges <- c(posEdgesA, posEdgesB, length(which(sparseA != 0)) +
length(which(sparseB != 0)) +
which(sparseP[which(contCIG != 0, arr.ind=TRUE)] > 0))
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font,
edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX),
rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.curved=curved,
edge.lty=igraph::E(gObj)$style, margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
if (side == "bottomleft"){
# create adjacency matrix
adjMat <- rbind(cbind(contCIG, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# width of the edges
Pslh <-sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
maxA <- max(abs(sparseA))
maxB <- max(abs(sparseB))
maxP <- max(abs(sparseP))
adjMatSlh <- rbind(cbind(Pslh/maxP, 0*sparseB, t(sparseA)/maxA),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)/maxB),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
# default node size and font size if not provided
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
} else {
edge.width <- edge.width * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
}
# arrow heads of curved edges should be zero width
curved <- rep(0, sum(adjMat))
slh <- which(adjMat[1, c(1:nrow(sparseP))]==1)
if (length(slh) > 0){ idCurved <- 1:length(slh) } else { idCurved <- numeric() }
for (j in 2:nrow(sparseP)){
slh <- which(adjMat[j, c(1:nrow(sparseP))]==1)
if (length(slh) > 0){
idCurved <- c(idCurved, 1:length(slh) + sum(adjMat[1:(j-1),]))
}
}
curved[idCurved] <- 1
# identify negative and positive edges
Pslh <-sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
adjMatSlh <- rbind(cbind(Pslh, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
diag(adjMatSlh) <- 0
edgeSigns <- sign(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
negEdges <- which(edgeSigns < 0)
posEdges <- which(edgeSigns > 0)
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font, edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX),
rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.curved=curved,
edge.lty=igraph::E(gObj)$style,
margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
}
if (type=="ABonly"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes of A and B
nNodesY <- nrow(sparseA)
nNodesX <- ncol(sparseB)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(6*(nrow(sparseA))^(-0.8), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseA))^(-0.7), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "Cross-time and covariate relations of VARX(1) model"
}
# specify plot layout
if (nrow(sparseA) %% 2 == 1){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2) + 1/2, length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2) + 1/2, nrow(sparseA) + 1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
if (nrow(sparseA) %% 2 == 0){
grid <- rbind(cbind(seq(0, -1, , length.out=nrow(sparseA)),
seq(0.5, floor(nrow(sparseA)/2), length.out=nrow(sparseA))),
cbind(seq(-1, 0, , length.out=ncol(sparseB)),
seq(ceiling(nrow(sparseA)/2 + 1), nrow(sparseA) + 1/2, length.out=ncol(sparseB))),
cbind(1, 1:nrow(sparseA)))
}
# create adjacency matrix
adjMat <- rbind(cbind(0*contCIG, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
adjMat[adjMat != 0] <- 1
# convert adjacency matrix to graph-object
gObj <- graph.adjacency(adjMat, mode="undirected")
# width of the edges
Pslh <- 0 * sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
maxA <- max(abs(sparseA))
maxB <- max(abs(sparseB))
maxP <- max(abs(sparseP))
adjMatSlh <- rbind(cbind(Pslh/maxP, 0*sparseB, t(sparseA)/maxA),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)/maxB),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
# size of the edges
if (edge.width <= 0){
edge.width <- 40 * (nrow(sparseA)^(-0.8)) * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
} else {
edge.width <- edge.width * abs(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
}
# identify negative and positive edges
Pslh <- 0*sparseP
Pslh[lower.tri(Pslh, diag=TRUE)] <- 0
adjMatSlh <- rbind(cbind(0*Pslh, 0*sparseB, t(sparseA)),
cbind(0*t(sparseB), matrix(0, ncol(sparseB), ncol(sparseB)), t(sparseB)),
cbind(0*sparseA, 0*sparseB, 0*contCIG))
diag(adjMatSlh) <- 0
edgeSigns <- sign(t(adjMatSlh)[which(t(adjMatSlh) != 0)])
negEdges <- which(edgeSigns < 0)
posEdges <- which(edgeSigns > 0)
# code sign of edges as solid/dashed
igraph::E(gObj)[negEdges]$style <- 2
igraph::E(gObj)[posEdges]$style <- 1
# make plot
plot(gObj,
edge.lty=0,
edge.arrow.size=0,
layout=grid,
vertex.shape="none",
vertex.color="white",
main=main,
margin=c(0, -0.5, 0.1, 0.3),
vertex.label.color="white", ...)
plot(gObj,
add=TRUE,
layout=grid,
vertex.size=rep(vertex.size, 2*nNodesY + nNodesX),
vertex.label.font=vertex.label.font, edge.width=edge.width,
vertex.color=c(rep(vertex.color.T0, nNodesY),
rep(vertex.color.X, nNodesX), rep(vertex.color.T1, nNodesY)),
vertex.frame.color=vertex.frame.color,
vertex.label=c(nNamesY, nNamesX, nNamesY),
vertex.label.cex=vertex.label.cex,
vertex.label.color=c(rep(vertex.label.color.T0, nNodesY),
rep(vertex.label.color.X, nNodesX),
rep(vertex.label.color.T1, nNodesY)),
edge.color="black",
edge.width=edge.width,
vertex.label.family="sans",
edge.lty=igraph::E(gObj)$style,
margin=c(0, -0.5, 0.1, 0.3), ...)
text(0, -1.2, expression(paste(Y[italic(t)], "", sep="")), cex=1.2, font=3)
text(0, 1.2, expression(paste(X[italic(t)], "", sep="")), cex=1.2)
text(1, -1.2, expression(paste(Y[italic(t)+1], "", sep="")), cex=1.2)
}
if (type=="contempPC"){
# prune covariate without connections (according to sparseA, sparseB and sparseP)
if (prune){
idRemoveA <- intersect(which(apply(sparseA, 1, function(Z){ all(Z == 0) })),
which(apply(sparseA, 2, function(Z){ all(Z == 0) })))
idRemoveBy <- which(apply(sparseB, 1, function(Z){ all(Z == 0) }))
idRemoveX <- which(apply(sparseB, 2, function(Z){ all(Z == 0) }))
diag(sparseP) <- 0
idRemoveP <- intersect(which(apply(sparseP, 1, function(Z){ all(Z == 0) })),
which(apply(sparseP, 2, function(Z){ all(Z == 0) })))
idRemoveY <- intersect(intersect(idRemoveA, idRemoveBy), idRemoveP)
if (length(idRemoveY) > 0){
sparseA <- sparseA[-idRemoveY, -idRemoveY]
sparseB <- sparseB[-idRemoveY, ]
sparseP <- sparseP[-idRemoveY, -idRemoveY]
nNamesY <- nNamesY[-idRemoveY]
}
if (length(idRemoveX) > 0){
sparseB <- sparseB[,-idRemoveX]
nNamesX <- nNamesX[-idRemoveX]
}
}
# store number of nodes
nNodes <- nrow(sparseP)
# default node size and font size if not provided
if (vertex.label.cex <= 0){
vertex.label.cex <- max(8*(nrow(sparseP))^(-0.6), 0.1)
}
if (vertex.size <= 0){
vertex.size <- max(75*(nrow(sparseP))^(-0.6), 1)
}
# default plot title if not provided
if (is.null(main)){
main <- "Contemp. cond. independence graph of VARX(1) model"
}
# get global CIG
CIG <- CIGofVAR1(sparseA, sparseP, type="contemp")
diag(CIG) <- 0
gObj <- graph.adjacency(CIG, "undirected")
# size of the edges
if (edge.width <= 0){ edge.width <- 10 * (nrow(sparseP)^(-0.8)) }
if (edge.width > 0){ edge.width <- edge.width }
# actual plotting
plot.igraph(gObj,
layout=layout.circle,
vertex.size=rep(vertex.size, nNodes),
vertex.label.font=vertex.label.font,
vertex.color=rep(vertex.color.X, nNodes),
vertex.frame.color=vertex.frame.color,
edge.color="black",
vertex.label=nNamesY,
vertex.label.cex=vertex.label.cex,
vertex.label.color=rep(vertex.label.color.X, nNodes),
edge.width=edge.width,
vertex.label.family="sans",
main=main, ...)
}
}
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