Question

I have the following code to plot the minimum spanning tree of a graph

## g is an igraph graph
mst = minimum.spanning.tree(g)
E(g)$color <- "SkyBlue2"

## how to I make mst a different color
E(g)[E(mst)]$color = "red"  ### <---- I WANT TO DO ESSENTIALLY THIS

plot(g,  edge.label=E(g)$weight)

That is, for a simple graph, I find the mst. I want to change the mst to red and plot the mst as part of the main graph. To do this, I want to select the edges of g that are also in mst. How do I do this?

---

UPDATE:

More generally, I have a graph g0 which is the mst of g, which has n vertices. It was constructed as follows

## implementing the Dijkstra-Prim algorithm
v0 = sample(1:n, 1)
g0 = graph.empty(n=n, directed=FALSE)
weight.g0 = 0
while(length(setdiff(1:n, v0) > 0)) {
  ## chose the shortest edge in the cut set of g

  ## to find the cut, figure out the set of edges where vertex is
  ## in v0 and the other is not
  cutset = E(g)[ v0 %->% setdiff(1:n, v0)]

  ## find the lightest weight edge
  cutweights = E(g)$weight[cutset]
  lightest_edge_idx = which(cutweights == min(cutweights))[1]
  weight.g0 = weight.g0 + min(cutweights)

  ## get the vertices of the lightest weight edge, add to path
  lightest_edge = cutset[as.numeric(cutset)[lightest_edge_idx]]
  vertices = get.edges(g, as.numeric(lightest_edge))

  g0 <- add.edges(g0, vertices, weight=min(cutweights))


  ## now that we have the vertices, add the one that is not in the
  ## graph already
  for(vtx in vertices) {
    if(!(vtx %in% v0)) {
      v0 = c(vtx, v0)
    }
  }

} 

I know I am probably not using a lot of useful features of igraph, but I do get g0 to be a mst at the end of this loop. Given this, I have

E(g0)
Edge sequence:

[1]   8 --  1
[2]   2 --  1
[3]   9 --  8
[4]   9 --  5
[5]   3 --  2
[6]   4 --  3
[7]   7 --  3
[8]  11 --  4
[9]   7 --  6
[10] 11 -- 10
> E(g)
Edge sequence:

[1]   2 --  1
[2]   5 --  1
[3]   8 --  1
[4]   3 --  2
[5]   5 --  2
[6]   6 --  2
[7]   4 --  3
[8]   6 --  3
[9]   7 --  3
[10]  7 --  4
[11] 11 --  4
[12]  6 --  5
[13]  8 --  5
[14]  9 --  5
[15]  7 --  6
[16]  9 --  6
[17] 10 --  6
[18] 10 --  7
[19] 11 --  7
[20]  9 --  8
[21] 10 --  9
[22] 11 -- 10

My question was, how do I assign an attribute to the edges in E(g) that are also in E(g0)?

Answer 1

This is actually quite easy because minimum.spanning.tree() keeps edge attributes. So you just need to assign an edge id attribute, and you’ll see which edges to color red. It goes like this:

# Some test data, no edge weights, quite boring
g <- erdos.renyi.game(20,2/20)
g
# IGRAPH U--- 20 24 -- Erdos renyi (gnp) graph
# + attr: name (g/c), type (g/c), loops (g/l), p (g/n)

E(g)$id <- seq_len(ecount(g))
mst <- minimum.spanning.tree(g)
mst
# IGRAPH U--- 20 18 -- Erdos renyi (gnp) graph
# + attr: name (g/c), type (g/c), loops (g/l), p (g/n), id (e/n)
E(mst)$id
# [1]  1  2  3  6  7  8  9 10 11 12 13 16 18 19 20 22 23 24

E(g)$color <- "black"
E(g)$color[E(mst)$id] <- "red"
plot(g)