Finding indirect nodes for every edge (in R)

Question

I have information on groups of physicians working together in given hospitals. A physician can work in more than one hospital at the same time. I would like to write a code that outputs information of all indirect colleagues of a given physician working in a given hospital. For instance, if I work in a given hospital with another physician who also works in another hospital, I would like to know who are the physicians with whom my colleague works in this other hospital.

Consider a simple example of three hospitals (1, 2, 3) and five physicians (A, B, C, D, E). Physicians A, B and C work together in hospital 1. Physicians A, B and D work together in hospital 2. Physicians B and E work together in hospital 3.

For each physician working in a given hospital I would like information of their indirect colleagues through each of their direct colleagues. For example, physician A has one indirect colleague through physician B in hospital 1: this is physician E in hospital 3. On the other hand, physician B does not have any indirect colleague through physician A in hospital 1. Physician C has two indirect colleagues through physician B in hospital 1: they are physician D in hospital 2 and physician E in hospital 3. And so on..

Below is the object that describes the nertworks of physicians in all hospitals:

edges <- tibble(hosp  = c("1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "3", "3"), 
             from = c("A", "A", "B", "B", "C", "C", "A", "A", "B", "B", "D", "D", "B", "E"), 
             to   = c("C", "B", "C", "A", "B", "A", "D", "B", "A", "D", "A", "B", "E", "B")) %>% arrange(hosp, from, to)

I would like a code that produces the following output:

output <- tibble(hosp     = c("1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3"), 
             from     = c("A", "A", "B", "B", "C", "C", "C", "A", "A", "B", "B", "D", "D", "D", "B", "E", "E", "E", "E"), 
             to       = c("C", "B", "C", "A", "B", "A", "B", "D", "B", "A", "D", "A", "B", "B", "E", "B", "B", "B", "B"),
             hosp_ind = c("" , "3", "" , "" , "2", "2", "3", "" , "3", "" , "" , "1", "1", "3", "" , "1", "1", "2", "2"),
             to_ind   = c("" , "E", "" , "" , "D", "D", "E", "" , "E", "" , "" , "C", "C", "E", "" , "A", "C", "A", "D")) %>% arrange(hosp, from, to)

Answer 1

Here is one option using igraph + data.table

library(igraph)
library(data.table)

g <- simplify(graph_from_data_frame(edges, directed = FALSE))
res <- setDT(edges)[
  ,
  c(.SD, {
    to_ind <- setdiff(
      do.call(
        setdiff,
        Map(names, ego(g, 2, c(to, from), mindist = 2))
      ), from
    )
    if (!length(to_ind)) {
      hosp_ind <- to_ind <- NA_character_
    } else {
      hosp_ind <- lapply(to_ind, function(v) names(neighbors(g, v)))
    }
    data.table(
      hosp_ind = unlist(hosp_ind),
      to_ind = rep(to_ind, lengths(hosp_ind))
    )
  }),
  .(id = seq(nrow(edges)))
][, id := NULL][]

and you will obtain

> res
    hosp from to hosp_ind to_ind
 1:    1    A  B        3      E
 2:    1    A  C     <NA>   <NA>
 3:    1    B  A     <NA>   <NA>
 4:    1    B  C     <NA>   <NA>
 5:    1    C  A        2      D
 6:    1    C  B        2      D
 7:    1    C  B        3      E
 8:    2    A  B        3      E
 9:    2    A  D     <NA>   <NA>
10:    2    B  A     <NA>   <NA>
11:    2    B  D     <NA>   <NA>
12:    2    D  A        1      C
13:    2    D  B        1      C
14:    2    D  B        3      E
15:    3    B  E     <NA>   <NA>
16:    3    E  B        1      A
17:    3    E  B        2      A
18:    3    E  B        1      C
19:    3    E  B        2      D

Also, when you run plot(g), you will see the graph like below