Creating Pairs by Group and Keep the Groups ids

Here below an example of what I would like:

From this data frame:

data<-data.frame(id_group=c("A","A","B","B","B","C","C", "C"),id_entity=c(1,2,2,3,4,2,5,1),nb_members=c(2,2,3,3,3,3,3,3))


  id_group id_entity nb_members
        A         1          2
        A         2          2
        B         2          3
        B         3          3
        B         4          3
        C         2          3
        C         5          3
        C         1          3

With the following code I manage to obtain the connections by pairs:

m <- crossprod(table(data[-3]))
m[upper.tri(m, diag = TRUE)] <-0
t_data<-subset(as.data.frame.table(m))
t_data <- t_data%>%subset(id_entity.1 != id_entity)

id_entity id_entity.1 Freq
         2           1    2
         3           1    0
         4           1    0
         5           1    1
         1           2    0
         3           2    1
         4           2    1
         5           2    1
         1           3    0
         2           3    0
         4           3    1
         5           3    0
         1           4    0
         2           4    0
         3           4    0
         5           4    0
         1           5    0
         2           5    0
         3           5    0
         4           5    0

However, I would like to keep the information about the groups ids in which the connections are made:

id_entity id_entity.1 Freq   id_group
         2           1    2    A,C
         3           1    0    NA
         4           1    0    NA
         5           1    1    C
         1           2    0    NA
         3           2    1    B
         4           2    1    B
         5           2    1    C
         1           3    0    NA
         2           3    0    NA
         4           3    1    B
         5           3    0    NA
         1           4    0    NA
         2           4    0    NA
         3           4    0    NA
         5           4    0    NA
         1           5    0    NA
         2           5    0    NA
         3           5    0    NA
         4           5    0    NA

Thank you very much for your help!

I accomplished this by making a table that mirrors the table used in crossprod(), but that has letters where there are non-zero values in the table of frequencies. Then, you can use information for id_identity and id_identity.1 to find the appropriate columns of the letter table. You want to past together the intersecting values from those two columns. You can replace the letter values with NA when the frequency count is zero.

library(dplyr)
d<-data.frame(id_group=c("A","A","B","B","B","C","C", "C"),id_entity=c(1,2,2,3,4,2,5,1),nb_members=c(2,2,3,3,3,3,3,3))

tab <- table(d[-3])
tab2 <- apply(tab, 2, function(x)ifelse(x == 1, rownames(tab), ""))
m <- crossprod(table(d[-3]))
m[upper.tri(m, diag = TRUE)] <-0
t_data<-as.data.frame.table(m)
t_data <- t_data%>%subset(id_entity.1 != id_entity)

t_data$pairs <- apply(t_data, 1, function(x)paste(intersect(tab2[,x[1]], tab2[,x[2]]), collapse=","))
t_data$pairs <- gsub("^\\,", "", t_data$pairs)
t_data$pairs <- ifelse(t_data$Freq == 0, NA, t_data$pairs)
t_data
#>    id_entity id_entity.1 Freq pairs
#> 2          2           1    2   A,C
#> 3          3           1    0  <NA>
#> 4          4           1    0  <NA>
#> 5          5           1    1     C
#> 6          1           2    0  <NA>
#> 8          3           2    1     B
#> 9          4           2    1     B
#> 10         5           2    1     C
#> 11         1           3    0  <NA>
#> 12         2           3    0  <NA>
#> 14         4           3    1     B
#> 15         5           3    0  <NA>
#> 16         1           4    0  <NA>
#> 17         2           4    0  <NA>
#> 18         3           4    0  <NA>
#> 20         5           4    0  <NA>
#> 21         1           5    0  <NA>
#> 22         2           5    0  <NA>
#> 23         3           5    0  <NA>
#> 24         4           5    0  <NA>

^{Created on 2023-05-17 with reprex v2.0.2}