Generate a unique set of complete undirected graphs from a tibble of nodes and sets

I have a tibble like this:

Nodes <- tibble(
  Set = c("A","A","A","B","B","C"),
  name = c(1,2,3,4,6,5)
)

I want to generate a graph that has Nodes as nodes set and

Edges <- tibble(
from = c(1,1,4),
to = c(2,3,6)
)

as edges. Of course I want to generalize this process for any Nodes. I think that I can code this with purrr, but I expect igraph to be faster and less tricky.

Theoretically, it would be nothing really different than:

Nodes %>% group_as(Set) %>% complete_graph(by = "name")

but I am not sure that a command like complete_graph() exists. It exists play_islands(), but it works differently and it assumes that n(Set) would be fixed.

Try make_full_graph from igraph

with(
  Nodes,
  do.call(
    rbind,
    Map(
      function(v) {
        get.data.frame(
          set_vertex_attr(
            make_full_graph(length(v)),
            name = "name", value = v
          )
        )
      },
      split(name, Set)
    )
  )
)

which gives

    from to
A.1    1  2
A.2    1  3
A.3    2  3
B      4  6