Identifying loops in a network diagram and converting this to node pathways in a dataframe

Question

I'm working with networks like these:

mat1 <- matrix(
  c(
    -1, -1, -1, 0, 0,
    1, -1, -1, 0, 0,
    1, 1, 0, -1, -1,
    0, 0, 1, -1, 0,
    0, 0, 1, 0, -1
  ),
  nrow = 5, ncol = 5, byrow = TRUE, 
  dimnames = list(NULL, c("N1", "N2", "A2", "Z3", "M"))
)

I'm trying to get all the loops into a dataframe broken into node pathways that form a loop like this:

out <- data.frame(
  from = c("N2", "N2", "Z3"),
  to = c("A2", "A2", "A2"),
  to1 = c("N2", "N1", "Z3"),
  to2 = c(NA, "N2", NA))

I've asked a similar question identifying pathways from specific nodes

but this is about extracting loops from the whole model regardless of which node you start with. The order isn't important so for example Z3 to A2 to Z3 is the same loop as A2 to Z3 to A2.

I'm very new to igraph, but I'm imagining that I would need something akin to:

lapply(V(g)[degree(g, mode = "out", loops = TRUE) > 0]

which was suggested in a comment on my previous post, but I'm unsure

I was able to find this which was helpful for the first part: stackoverflow.com/questions/55091438/r-igraph-find-all-cycles — Hard_Course
– Hard_Course, Commented Mar 26 at 19:40

ThomasIsCoding · Accepted Answer · 2025-03-27 23:21:44Z

Given matrix mat1, you can try the code below

mat1 %>%
  `<`(0) %>%
  graph_from_adjacency_matrix(
    mode = "directed"
  ) %>%
  as_data_frame() %>%
  mutate(id = row_number(), .by = from) %>%
  pivot_wider(
    names_from = id,
    names_glue = "to{id}",
    values_from = to
  )

which gives

# A tibble: 5 × 4
  from  to1   to2   to3  
  <chr> <chr> <chr> <chr>
1 N1    N1    N2    A2
2 N2    N2    A2    NA
3 A2    Z3    M     NA
4 Z3    Z3    NA    NA
5 M     M     NA    NA

If you care the vertices that have loops only, you can try

mat1 %>%
  `<`(0) %>%
  graph_from_adjacency_matrix(
    mode = "directed"
  ) %>%
  as_data_frame() %>%
  filter(from %in% {
    filter(., from == to) %>% pull(from)
  }) %>%
  mutate(id = row_number(), .by = from) %>%
  pivot_wider(
    names_from = id,
    names_glue = "to{id}",
    values_from = to
  )

such that

# A tibble: 4 × 4
  from  to1   to2   to3  
  <chr> <chr> <chr> <chr>
1 N1    N1    N2    A2
2 N2    N2    A2    NA
3 Z3    Z3    NA    NA
4 M     M     NA    NA

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