How to add a edges between component of a graph in igraph R

Question

I have a graph containing 4 components. Now, I want to add an edge among all components based on the size of the membership.

For example, the following graph contains 4 components.

First, I will connect all components with only one edge and take the edge randomly. I can do it using this code

graph1 <- graph_from_data_frame(g, directed = FALSE)
E(graph1)$weight <- g$new_ssp
cl <- components(graph1)

graph2 <- with(
  stack(membership(cl)),
  add.edges(
    graph1,
    c(combn(sapply(split(ind, values), sample, size = 1), 2)),
    weight = runif(choose(cl$no, 2))
  )
)

Secondly, now, I want to add an edge between component-1 and component-2. I want to add an edge between 2 components but rest of the component will be present in the new graph from the previous graph.

Like, after adding an edge between component-1 and component-2, the new graph will contain 3 component 1st (component-1 and component-2 as a 1 component because we added 1 edge), 2nd (component-3 from the main graph), and 3rd (component-4 from the main graph). I can do it using this code

dg <- decompose.graph(graph1)
graph3 <- (dg[[1]] %u% dg[[2]])

component_subgraph_1 <- components(graph3)

graph2 <- with(
  stack(membership(component_subgraph_1)),
  add.edges(
    graph1,
    c(combn(sapply(split(ind, values), sample, size = 1), 2)),
    weight = 0.01))

Figure:

Same for all combinations. Such as, component-1 and component-3, and component-1 and component-4, and component-2 and component-3, and component-2 and component-4, and component-3 and component-4.

But, this is not feasible to write the code and change manually dg[[1]], dg[[2]], and so on. Moreover, my actual dataset contains a lot of components. So, in reality, this is impossible. Any idea, how can I do this automatically?

Actually, I have a scoring function (like the shortest path). So, I want to check the score after adding all components, or after adding only 2 components, after adding only 3 components, and so on! Something like greedy algorithms.

Reproducible Data:

g <- structure(list(query = structure(c(1L, 1L, 1L, 2L, 2L, 3L, 4L, 
                                   5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L), .Label = c("ID_00104", 
                                                                                                       "ID_00136", "ID_00169", "ID_00178", "ID_00180"), class = "factor"), 
               target = structure(c(16L, 19L, 20L, 1L, 9L, 9L, 6L, 11L, 
                                    13L, 15L, 4L, 8L, 10L, 14L, 2L, 3L, 5L, 7L, 12L, 17L, 18L
               ), .Label = c("ID_00169", "ID_00288", "ID_00324", "ID_00394", 
                             "ID_00663", "ID_00790", "ID_00846", "ID_00860", "ID_00910", "ID_00959", 
                             "ID_01013", "ID_01047", "ID_01130", "ID_01222", "ID_01260", "ID_06663", 
                             "ID_06781", "ID_06786", "ID_06791", "ID_09099"), class = "factor"), 
               new_ssp = c(0.654172560113154, 0.919096895578551, 0.925821596244131, 
                           0.860406091370558, 0.746376811594203, 0.767195767195767, 
                           0.830379746835443, 0.661577608142494, 0.707520891364902, 
                           0.908193484698914, 0.657118786857624, 0.687664041994751, 
                           0.68586387434555, 0.874513618677043, 0.836646499567848, 0.618361836183618, 
                           0.684163701067616, 0.914728682170543, 0.876297577854671, 
                           0.732707087959009, 0.773116438356164)), row.names = c(NA, 
                                                                                 -21L), class = "data.frame")

Thanks in advance.

Answer 1

You are actually close to what you want already. Perhaps the code below could help you

out <- with(
  stack(membership(cl)),
  lapply(
    combn(split(ind, values), 2, simplify = FALSE),
    function(x) {
      add.edges(
        graph1,
        c(combn(sapply(x, sample, size = 1), 2)),
        weight = 0.01
      )
    }
  )
)

and then you can run

sapply(out, plot)

to visualize all the combinations.