How to iterate with dynamic changing the number edges and nodes? - r

Question

I have a random graph with 10 nodes where 4 nodes have the zero degree.
It is required to obtain the connected graph by 1) select a node with zero degree and a minimal feature (for exmaple, random number from uniform distribautin) corresponding to each edge and connect it with graph by creation two incident edges to the node and deleting the 3rd edge, 2) repeat step 1 for all zero degree nodes.
The original graph in left, the resulting one in right.
My attempt is:
library(igraph)
######################################################################
set.seed(5)
g <- sample_gnm(10, 4)
xy <- cbind(runif(10), runif(10))
par(mfrow=c(1,2))
plot(g, vertex.size=5, layout=xy)
num_point <- length(V(g)[degree(g)==0])
for(k in 1:num_point){
points = V(g)[degree(g)==0]
for(i in 1:length(E(g))) { # loop over all edges
head <- get.edgelist(g)[i,][1]; h <- c(V(g)[head]$x, V(g)[head]$y)
tail <- get.edgelist(g)[i,][2]; t <- c(V(g)[tail]$x, V(g)[tail]$y)
d <- NULL
# loop over all points
for(j in points) d <- c(d, runif(1))
E(g)[i]$d <- min(d) # local min
E(g)[i]$p <- points[which(d == min(d))]
} # i
ei = which.min(E(g)$d) # edge with the global min
vi = E(g)[ei]$p
# head and tail of edge with global min
head <- get.edgelist(g)[E(g)[ei],][1]; tail <- get.edgelist(g)[E(g)[ei],][2]
g <- add_edges(g, c(head, V(g)[vi],
V(g)[vi],
tail));
g <- delete_edges(g, get.edge.ids(g, c(head, tail) ))
}
plot(g, vertex.size=5, layout=xy)
Question. How to organize the loop over all edges when the number of edges increase by 1 and number of point decrising by 1 evety step? One can see, I don't use the k variable in explicit form.

Answer 1

Instead of for loop, I think you can use repeat plus a termination condition, i.e., no isolated vertices any more
repeat {
points <- V(g)[degree(g) == 0]
for (i in 1:length(E(g))) { # loop over all edges
head <- get.edgelist(g)[i, ][1]
h <- c(V(g)[head]$x, V(g)[head]$y)
tail <- get.edgelist(g)[i, ][2]
t <- c(V(g)[tail]$x, V(g)[tail]$y)
d <- NULL
# loop over all points
for (j in points) d <- c(d, runif(1))
E(g)[i]$d <- min(d) # local min
E(g)[i]$p <- points[which(d == min(d))]
} # i
ei <- which.min(E(g)$d) # edge with the global min
vi <- E(g)[ei]$p
# head and tail of edge with global min
head <- get.edgelist(g)[E(g)[ei], ][1]
tail <- get.edgelist(g)[E(g)[ei], ][2]
g <- add_edges(g, c(
head, V(g)[vi],
V(g)[vi],
tail
))
g <- delete_edges(g, get.edge.ids(g, c(head, tail)))
if (sum(degree(g) == 0) == 0) {
break
}
}

Answer 2

I will recommend you to use recursion for this and drop for loop- using recursion for tree and graph structures will definitely make your life easier.
Answer:
maintain a stack of all the leaf nodes
every time you iterate empty your stack by matching the leaf node values
if there's a new value and count of the stack != to old count.
Now iterate again.