Add a method to return all-paths through a graph

graph.lisp

@@ -160,6 +160,8 @@
    :closedp
    :clustering-coefficient
    :cliques
+   ;; All paths
+   :all-paths
    ;; Shortest Path
    :shortest-path
    ;; Max Flow
@@ -1053,6 +1055,19 @@ The Bron-Kerbosh algorithm is used."))
     (bron-kerbosch nil (nodes graph) nil))
   cliques)
 
+(defgeneric all-paths (graph a b)
+  (:documentation "Return all paths in GRAPH from A to B.")
+  (:method ((graph graph) a b)
+    (labels
+        ((step-path (from to visited)
+           (if (equal from to)
+               (list (list to))
+               (mapcar {cons from}
+                       (mappend {step-path _ to (cons from visited)}
+                                (set-difference (neighbors graph from)
+                                                visited))))))
+      (step-path a b nil))))
+
 
 ;;; Shortest Path
 (defgeneric shortest-path (graph a b &optional heuristic)

test.lisp

@@ -362,6 +362,12 @@
                    '((:Q :S :R) (:C :S) (:A :C :B))
                    :test #'set-equal))))
 
+(deftest all-path-between-foo-and-baz-or-qux ()
+  (with-fixture normal-graph
+    (is (set-equal (all-paths *graph* 'a 'f)
+                   '((a b c d e f) (a b c e f) (a b f))
+                   :test #'equalp))))
+
 (deftest shortest-path-between-foo-and-baz-or-qux ()
   (with-fixture less-small-graph
     (is (tree-equal (shortest-path (digraph-of *graph*) :foo :baz)