Retrieve list of path name from igraph all_simple_paths - r

Question

I have a directed cyclical matrix and need to extract all the simple paths between any i and j.
The following is my ex. matrix:
>M2<-matrix(c(1,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0,1,1), 5, byrow=T)
>colnames(M2)<-c("A", "B", "C", "D", "E")
>row.names(M2)=colnames(M2)
>M2
A B C D E
A 1 1 0 0 0
B 1 1 1 1 0
C 0 1 1 1 0
D 0 1 0 1 1
E 0 0 0 1 1
I use igraph to convert the matrix to a graph object using the graph_from_adjency_matrix function.
>graph<-graph_from_adjacency_matrix(M2, mode=c("directed"), weighted=NULL, diag=F, add.colnames=NULL, add.rownames=NA)
>graph
IGRAPH DN-- 5 9 --
+ attr: name (v/c)
+ edges (vertex names):
[1] A->B B->A B->C B->D C->B C->D D->B D->E E->D
And from there I use the all_simple_paths function to get all the simple paths between i and j. And here starts my questions.
1) I can specify the j (argument to has to=V(graph)) to be all possible end vertices. But I can't specify the from argument to calculate the paths looking for all vertices has possible starting points. I have to specify each of my variables at a time. Any solution?
2) The all_simple_path function works well and gives me all the simple paths between i and j, e.g. for simple paths starting in A and ending in any possible j:
>Simple_path_list<-all_simple_paths(graph, from ="A", to=V(graph), mode = c("out"))
>Simple_path_list
[[1]]
+ 2/5 vertices, named:
[1] A B
[[2]]
+ 3/5 vertices, named:
[1] A B C
[[3]]
+ 4/5 vertices, named:
[1] A B C D
[[4]]
+ 5/5 vertices, named:
[1] A B C D E
[[5]]
+ 3/5 vertices, named:
[1] A B D
[[6]]
+ 4/5 vertices, named:
[1] A B D E
My problem is, I need to collect all those paths and put on a list, e.g.:
Paths
A B
A B C
A B C D
A B C D E
A B D
A B D E
I tried to create a list and call for the path names using the normal list<-Simple_path_list[1] or so, but I always retrieve, together with the paths, the information on the number of vertices involved (e.g., + 4/5 vertices, named). Any idea on how can I retrieve solely the paths name and not the other information?

Answer 1

The lapply function on all_simple_paths makes a list of lists (i.e. a list of each vertex's list of paths). Simplify the list of lists to a list using unlist(..., recursive = F) and then use names or igraph's as_ids to extract the vertex ids solo.
library(igraph)
M2<-matrix(c(1,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0,1,1), 5, byrow=T)
colnames(M2)<-c("A", "B", "C", "D", "E")
row.names(M2)=colnames(M2)
M2
graph<-graph_from_adjacency_matrix(M2, mode=c("directed"), weighted=NULL, diag=F, add.colnames=NULL, add.rownames=NA)
l <- unlist(lapply(V(graph) , function(x) all_simple_paths(graph, from=x)), recursive = F)
paths <- lapply(1:length(l), function(x) as_ids(l[[x]]))
This produces:
> paths
[[1]]
[1] "A" "B"
[[2]]
[1] "A" "B" "C"
[[3]]
[1] "A" "B" "C" "D"
[[4]]
[1] "A" "B" "C" "D" "E"
[[5]]
[1] "A" "B" "D"
[[6]]
[1] "A" "B" "D" "E"
[[7]]
[1] "B" "A"
[[8]]
[1] "B" "C"
[[9]]
[1] "B" "C" "D"
[[10]]
[1] "B" "C" "D" "E"
[[11]]
[1] "B" "D"
[[12]]
[1] "B" "D" "E"
[[13]]
[1] "C" "B"
[[14]]
[1] "C" "B" "A"
[[15]]
[1] "C" "B" "D"
[[16]]
[1] "C" "B" "D" "E"
[[17]]
[1] "C" "D"
[[18]]
[1] "C" "D" "B"
[[19]]
[1] "C" "D" "B" "A"
[[20]]
[1] "C" "D" "E"
[[21]]
[1] "D" "B"
[[22]]
[1] "D" "B" "A"
[[23]]
[1] "D" "B" "C"
[[24]]
[1] "D" "E"
[[25]]
[1] "E" "D"
[[26]]
[1] "E" "D" "B"
[[27]]
[1] "E" "D" "B" "A"
[[28]]
[1] "E" "D" "B" "C"
Addition
For all_shortest_paths you must subset the list of paths for each node to exclude the geodesic information.
l <- lapply(V(graph), function(x) all_shortest_paths(graph, from = x))
l <- lapply(l, function(x) x[[-2]])
l <- unlist(l, recursive = F)
paths <- lapply(1:length(l), function(x) as_ids(l[[x]]))