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