diff --git a/lib/graph/graph.hpp b/lib/graph/graph.hpp
index ca99b0a..4f6e8b2 100644
--- a/lib/graph/graph.hpp
+++ b/lib/graph/graph.hpp
@@ -123,6 +123,7 @@ public:
 
 private:
 
+  std::vector<value_type>& nonConstNeighboursOf(const_reference data);
   static void eraseEdge(edge_container& v, const_reference data);
 
   v_container m_vertices;
@@ -183,14 +184,18 @@ inline void Graph<V>::removeVertex(const_reference data)
 template <typename V>
 inline void Graph<V>::modifyVertex(const_reference old_data, const_reference new_data)
 {
+  if (old_data == new_data)
+    return;
+
   v_iterator it = m_vertices.find(old_data);
   if (it == m_vertices.end())
     return;
 
   std::vector<value_type> neighbours = neighboursOf(old_data);
   for (auto &v : neighbours) {
-    std::vector<value_type>::iterator n_it = neighbours.find(old_data);
-    *it = new_data;
+    std::vector<value_type>& n_v = nonConstNeighboursOf(v);
+    typename std::vector<value_type>::iterator n_it = std::find(n_v.begin(), n_v.end(), old_data);
+    *n_it = new_data;
   }
 
   m_vertices.erase(it);
@@ -256,6 +261,13 @@ inline std::vector<V> Graph<V>::neighboursOf(const_reference data) const
     return vertex_it->second;
 }
 
+template <typename V>
+inline std::vector<V>& Graph<V>::nonConstNeighboursOf(const_reference data)
+{
+  v_iterator vertex_it = m_vertices.find(data);
+  return vertex_it->second;
+}
+
 template <typename V>
 inline std::vector<typename Graph<V>::Edge> Graph<V>::edges() const
 {
diff --git a/lib/graph/graph_xml.hpp b/lib/graph/graph_xml.hpp
index 25af7a0..169ff03 100644
--- a/lib/graph/graph_xml.hpp
+++ b/lib/graph/graph_xml.hpp
@@ -1,4 +1,4 @@
-#include <graph.hpp>
+#include "graph.hpp"
 
 #include <stdexcept>
 #include <fstream>
@@ -20,19 +20,24 @@ void readVertices(Graph<V>& g,  F vertexCreator, const xmlNodePtr root_element)
       std::vector<V> edges;
       for (xmlNodePtr cur_kid = cur_node->children; cur_kid; cur_kid = cur_kid->next)
         if (cur_kid->type == XML_ELEMENT_NODE && cur_kid->children->type == XML_TEXT_NODE) {
-          const std::string e( reinterpret_cast<const char*>(cur_kid->children->content));
-          edges.push_back(vertexCreator(e));
+          const std::string edge( reinterpret_cast<const char*>(cur_kid->children->content));
+          V e = vertexCreator(edge);
+          edges.push_back(e);
         }
-
       g.setEdges(v, edges);
     }
 }
 
 } // anonym namespace
 
+
 template <typename V, typename F>
 Graph<V> readGraphFromXML(const std::string& filename, F vertexCreator)
 {
+  std::ifstream file(filename);
+  if (!file.good())
+    throw std::runtime_error("Failed to open " + filename + " to read.");
+
   xmlDocPtr doc = xmlReadFile(filename.c_str(), NULL, 0);
   if (doc == NULL)
     throw std::runtime_error("Failed to parse " + filename);
@@ -64,7 +69,7 @@ void writeGraphToXML(const Graph<V>& g, const std::string& filename, F vertexSer
     file << "<vertex pos=\"" << v << "\">" << std::endl;
     for (const auto cit2 : g.neighboursOf(cit)) {
       const std::string n = vertexSerializer(cit2);
-      file << "  <edge>" << v << "</edge>" << std::endl;
+      file << "  <edge>" << n << "</edge>" << std::endl;
     }
     file << "</vertex>" << std::endl;
   }