I have a bipartite graph and I want the projections of this graph to have edge attributes that record via which nodes they were connected. For example:

require(igraph)
set.seed(123)
g <- sample_bipartite(5, 5, p =.5)
V(g)$name <- c(letters[1:5], 1:5)
g1 <- bipartite_projection(g)[[1]]
g2 <- bipartite_projection(g)[[2]]

par(mfrow = c(1, 3))
plot(g,
     vertex.shape = ifelse(V(g)$type == FALSE, "square", "circle"),
     vertex.color = ifelse(V(g)$type == FALSE, "gold", "tomato"),
     main = "Bipartite")
plot(g1,
     main = "Projection 1")
plot(g2,
     main = "Projection 2")
par(mfrow = c(1, 1))

I want the information that I added by hand to the plot to be in the network object. It it easily done in igraph? Thanks.

With bipartite_projection

If you really want ot use bipartite_projection, you can try to define your custom function f like below:

f <- function(gp) {
  df <- get.data.frame(gp)[1:2]
  df$lbl <- apply(
    df,
    1,
    function(v) {
      max(do.call(intersect, unname(lapply(v, function(x) names(neighbors(g, x))))))
    }
  )
  res <- graph_from_data_frame(df, directed = FALSE)
  plot(res, edge.label = E(res)$lbl)
}

f(g1)
f(g2)

which gives

Without bipartite_projection

Below is an option without using bipartite_projection (take g1 as the an example, and g2 can be obtained in a similar way)

g1 <- simplify(
  graph_from_data_frame(
    do.call(
      rbind,
      lapply(
        Filter(
          function(x) nrow(x) > 1,
          split(get.data.frame(g), ~to)
        ),
        function(d) {
          with(
            d,
            cbind(data.frame(t(combn(from, 2))), weight = unique(to))
          )
        }
      )
    ),
    directed = FALSE
  ),
  edge.attr.comb = "max"
)

and plot(g1, edge.label = E(g1)$weight) gives