diff --git a/src/edmonds.cpp b/src/edmonds.cpp
index 50b1529..d5a8073 100644
--- a/src/edmonds.cpp
+++ b/src/edmonds.cpp
@@ -9,12 +9,46 @@ void check_integrity(Graph const & graph)
 {
    for(NodeId id = 0; id < graph.num_nodes(); ++id)
    {
+      // Check that μ encodes a valid matching
       NodeId matched = graph.matched_neighbor(id);
       if(matched != id)
       {
          assert(graph.matched_neighbor(matched) == id);
       }
 
+      if (graph.is_out_of_forest(id))
+      {
+         assert(graph.phi(id) == id);
+         assert(graph.rho(id) == id);
+      }
+      else
+      {
+         // check for a path to the root, i.e. ρ(node)
+         NodeId cur_node = id;
+         while(cur_node != graph.rho(cur_node))
+         {
+            // If the condition was true, then cur_node is outer, part of a blossom
+            // and we want to follow its path
+            // therefore, we check that both φ and μ are not the identity on this node
+            // and point to vertices that have the same rho
+            assert(graph.matched_neighbor(cur_node) != cur_node);
+            assert(graph.phi(cur_node) != cur_node);
+            assert(graph.rho(graph.matched_neighbor(cur_node)) == graph.rho(cur_node));
+            assert(graph.rho(graph.phi(cur_node)) == graph.rho(cur_node));
+
+            // now, walk along the matched edge
+            cur_node = graph.matched_neighbor(cur_node);
+
+            // now we want to walk along φ, this will again
+            // - not be the identity
+            // - result in a node that has the same rho
+            assert(graph.phi(cur_node) != cur_node);
+            assert(graph.rho(graph.phi(cur_node)) == graph.rho(cur_node));
+
+            cur_node = graph.matched_neighbor(graph.phi(cur_node));
+         }
+      }
+
       if (not graph.is_outer(id))
       {
          assert(graph.rho(id) == id);