diff --git a/lib/spack/spack/graph.py b/lib/spack/spack/graph.py
index 063e4647b60..6a80c7d4725 100644
--- a/lib/spack/spack/graph.py
+++ b/lib/spack/spack/graph.py
@@ -94,6 +94,7 @@ def topological_sort(spec, **kwargs):
     nodes = spec.index()
 
     topo_order = []
+    par = {name: parents(nodes[name]) for name in nodes.keys()}
     remaining = [name for name in nodes.keys() if not parents(nodes[name])]
     heapify(remaining)
 
@@ -102,12 +103,12 @@ def topological_sort(spec, **kwargs):
         topo_order.append(name)
 
         node = nodes[name]
-        for dep in children(node).values():
-            del parents(dep)[node.name]
-            if not parents(dep):
+        for dep in children(node):
+            par[dep.name].remove(node)
+            if not par[dep.name]:
                 heappush(remaining, dep.name)
 
-    if any(parents(s) for s in spec.traverse()):
+    if any(par.get(s.name, []) for s in spec.traverse()):
         raise ValueError("Spec has cycles!")
     else:
         return topo_order
@@ -477,8 +478,8 @@ def write(self, spec, **kwargs):
 
                 # Replace node with its dependencies
                 self._frontier.pop(i)
-                if node.dependencies:
-                    deps = sorted((d for d in node.dependencies), reverse=True)
+                if node.dependencies():
+                    deps = sorted((d.name for d in node.dependencies()), reverse=True)
                     self._connect_deps(i, deps, "new-deps") # anywhere.
 
                 elif self._frontier:
diff --git a/lib/spack/spack/spec.py b/lib/spack/spack/spec.py
index c6277fc8d2b..8e44075f42f 100644
--- a/lib/spack/spack/spec.py
+++ b/lib/spack/spack/spec.py
@@ -460,7 +460,7 @@ def concrete(self):
 
     def __str__(self):
         return ''.join(
-            ["^" + str(self[name].spec) for name in sorted(self.keys())])
+            ["^" + self[name].format() for name in sorted(self.keys())])
 
 
 @key_ordering
@@ -861,7 +861,7 @@ def return_val(res):
             for name in sorted(successors):
                 child = successors[name]
                 children = child.spec.traverse_with_deptype(
-                    visited, d=d + 1, deptype=deptype_query,
+                    visited, d=d + 1, deptype=deptype,
                     deptype_query=deptype_query,
                     _self_deptype=child.deptypes, **kwargs)
                 for elt in children: