Question

Given a graph G, a node n and a length L, I’d like to collect all (non-cyclic) paths of length L that depart from n.

Do you have any idea on how to approach this?

By now, I my graph is a networkx.Graph instance, but I do not really care if e.g. igraph is recommended.

Thanks a lot!

Answer 1

I would just like to expand on Lance Helsten’s excellent answer:

The depth-limited search searches for a particular node within a certain depth (what you’re calling the length L), and stops when it finds it. If you will take a look at the pseudocode in the wiki link in his answer, you’ll understand this:

DLS(node, goal, depth) {
  if ( depth >= 0 ) {
    if ( node == goal )
      return node

    for each child in expand(node)
      DLS(child, goal, depth-1)
  }
}

In your case, however, as you’re looking for all paths of length L from a node, you will not stop anywhere. So the pseudocode must be modified to:

DLS(node, depth) {
    for each child in expand(node) {
      record paths as [node, child]
      DLS(child, depth-1)
    }
}

After you’re done with recording all the single-link paths from successive nests of the DLS, just take a product of them to get the entire path. The number of these gives you the number of paths of the required depth starting from the node.