How to define the mapping parameter iteratively to contract vertices chains?

Question

I have a simple graph g. It is requared to smoth the graph by deleting the vertices whose degree is 2 with preserving the layout of the original graph. The same task was solved in the Mathematica.

library(igraph)
set.seed(1)
# preprocessing
g          <- sample_gnp(40, 1/20)
V(g)$name  <- seq(1:vcount(g))
components <- clusters(g, mode="weak")
biggest_cluster_id <- which.max(components$csize)
vert_ids           <- V(g)[components$membership == biggest_cluster_id]
vert_ids

# input random graph
g    <- induced_subgraph(g, vert_ids)
LO = layout.fruchterman.reingold(g)
plot(g, vertex.color = ifelse(degree(g)==2, "red", "green"), main ="g", layout = LO)

I have selected vertices chains with a degree of 2.

subg     <- induced_subgraph(g, degree(g)==2)
subg_ids <- V(subg); subg_ids

I have read the Q&A and I manually define the mapping parameter of the contract() function.

# join nodes 3 -> 14, 15 -> 40, 13 -> 31, 29 -> 6
mapping = c(2, 3, 4, 5, 6, 7, 8, 10, 13, 3, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 6, 30, 13, 32, 33, 34, 35, 36, 38, 39, 15)

g2 <- simplify(contract(g, mapping=mapping, vertex.attr.comb=toString))
# L2 <- LO[-as.numeric(c(14, 40, 31, 6)),] # not working
plot(g2, vertex.color = ifelse(degree(g2)==2, "red", "green"), main ="g2")

Question. What is a possible way to define the mapping parameter iteratively?

In the expected result, why is there no edge between nodes 6 and 31? All the other "degree-2-components" have been replaced by an edge. — AEF, Aug 19 '21 at 10:06

AEF · Answer 1 · 2021-08-19T11:08:19.850

This is only a partial answer, since it does not give a way to compute the contraction automatically. However, I can give some insights on the manual mapping:

Your vertices have names, so those are used for reference instead of the internal vertex number from 1 to n. In the mapping we need to give the new IDs of the vertices after the contraction.

The original IDs are

> V(g)
+ 33/33 vertices, named, from 0af52c3:
  [1] 2  3  4  5  6  7  8  10 13 14 15 16 17 18 19 20 21 22 23 25 26 27 29 30 31 32 33 34 35 36 38 39 40

The new IDs can be given as (multiple possibilities exist):

mapping <- c(6, 14, 6, 5, 6, 7, 7, 10, 31, 14, 15, 16, 17, 14, 6, 7, 31, 22, 6, 25, 26, 27, 14, 30, 31, 6, 6, 34, 35, 36, 38, 39, 15)

For better overview:

old ID:   2  3 4 5 6 7 8 10 13 14 15 16 17 18 19 20 21 22 23 25 26 27 29 30 31 32 33 34 35 36 38 39 40
new ID:   6 14 6 5 6 7 7 10 31 14 15 16 17 14  6  7 31 22  6 25 26 27 14 30 31  6  6 34 35 36 38 39 15

This results in:

g2 <- simplify(contract(g, mapping=mapping, vertex.attr.comb=toString))
plot(g2, vertex.color = ifelse(degree(g2)==2, "red", "green"), main ="g2")

To get rid of the now existing degree-0-nodes you can do:

g3 <- delete.vertices(g2, which(degree(g2) == 0))

Alternatively, and maybe even cleaner you could delete nameless nodes:

g3 <- delete.vertices(g2, which(names(V(g2)) == ""))

To keep the original layout you can do:

L3 <- LO[-which(mapping != as.numeric(names(V(g)))),]
plot(g3, layout = L3)

But is not very good looking in this case...

Thank for the partical answer, I have tried to reorder the layout L3 <- LO[-unique(mapping),]; plot(g3, layout = L3), but it is not correct. — Nick, Aug 19 '21 at 10:55
Where is the error? I have compared it to your expected result and it was isomorphic? — AEF, Aug 19 '21 at 10:57
I mean of course it looks different, but the structure is extactly as expected. — AEF, Aug 19 '21 at 10:59
No error, structure is same, but it is requred to restore coodinates too. — Nick, Aug 19 '21 at 11:02

ThomasIsCoding · Accepted Answer · 2021-08-19T11:10:32.917

Here is an option without mapping in contract (so you don't need to configure mapping manually)

g2 <- graph_from_data_frame(
  rbind(
    get.data.frame(delete.vertices(g, names(subg_ids))),
    do.call(
      rbind,
      lapply(
        decompose(subg),
        function(x) {
          nbs <- names(unlist(neighborhood(g, nodes = names(V(x))[degree(x) < 2])))
          setNames(data.frame(t(subset(nbs, !nbs %in% names(subg_ids)))), c("from", "to"))
        }
      )
    )
  ),
  directed = FALSE
)

and you will see the graph below after running

plot(g2, main = "g2", layout = LO[match(names(V(g2)), names(V(g))), ])

How to define the mapping parameter iteratively to contract vertices chains?

2 Answers2