diff --git a/lemon/bits/graph_extender.h b/lemon/bits/graph_extender.h
--- a/lemon/bits/graph_extender.h
+++ b/lemon/bits/graph_extender.h
@@ -56,11 +56,11 @@
       return Parent::maxArcId();
     }
 
-    Node fromId(int id, Node) const {
+    static Node fromId(int id, Node) {
       return Parent::nodeFromId(id);
     }
 
-    Arc fromId(int id, Arc) const {
+    static Arc fromId(int id, Arc) {
       return Parent::arcFromId(id);
     }
 
@@ -355,15 +355,15 @@
       return Parent::maxEdgeId();
     }
 
-    Node fromId(int id, Node) const {
+    static Node fromId(int id, Node) {
       return Parent::nodeFromId(id);
     }
 
-    Arc fromId(int id, Arc) const {
+    static Arc fromId(int id, Arc) {
       return Parent::arcFromId(id);
     }
 
-    Edge fromId(int id, Edge) const {
+    static Edge fromId(int id, Edge) {
       return Parent::edgeFromId(id);
     }
 
diff --git a/lemon/edge_set.h b/lemon/edge_set.h
--- a/lemon/edge_set.h
+++ b/lemon/edge_set.h
@@ -867,7 +867,7 @@
       arc.id = arcs.size() - 1;
     }
 
-    void next(Arc& arc) const {
+    static void next(Arc& arc) {
       --arc.id;
     }
 
@@ -1173,7 +1173,7 @@
       arc.id = arcs.size() - 1;
     }
 
-    void next(Arc& arc) const {
+    static void next(Arc& arc) {
       --arc.id;
     }
 
@@ -1181,7 +1181,7 @@
       arc.id = arcs.size() / 2 - 1;
     }
 
-    void next(Edge& arc) const {
+    static void next(Edge& arc) {
       --arc.id;
     }
 
diff --git a/lemon/full_graph.h b/lemon/full_graph.h
--- a/lemon/full_graph.h
+++ b/lemon/full_graph.h
@@ -51,7 +51,7 @@
     typedef True ArcNumTag;
 
     Node operator()(int ix) const { return Node(ix); }
-    int index(const Node& node) const { return node._id; }
+    static int index(const Node& node) { return node._id; }
 
     Arc arc(const Node& s, const Node& t) const {
       return Arc(s._id * _node_num + t._id);
@@ -209,7 +209,7 @@
     /// digraph its nodes can be indexed with integers from the range
     /// <tt>[0..nodeNum()-1]</tt>.
     /// \sa operator()
-    int index(const Node& node) const { return Parent::index(node); }
+    static int index(const Node& node) { return Parent::index(node); }
 
     /// \brief Returns the arc connecting the given nodes.
     ///
@@ -283,7 +283,7 @@
   public:
 
     Node operator()(int ix) const { return Node(ix); }
-    int index(const Node& node) const { return node._id; }
+    static int index(const Node& node) { return node._id; }
 
     Edge edge(const Node& u, const Node& v) const {
       if (u._id < v._id) {
@@ -580,7 +580,7 @@
     /// graph its nodes can be indexed with integers from the range
     /// <tt>[0..nodeNum()-1]</tt>.
     /// \sa operator()
-    int index(const Node& node) const { return Parent::index(node); }
+    static int index(const Node& node) { return Parent::index(node); }
 
     /// \brief Returns the arc connecting the given nodes.
     ///
diff --git a/lemon/hypercube_graph.h b/lemon/hypercube_graph.h
--- a/lemon/hypercube_graph.h
+++ b/lemon/hypercube_graph.h
@@ -262,7 +262,7 @@
       return arc._id >> _dim;
     }
 
-    int index(Node node) const {
+    static int index(Node node) {
       return node._id;
     }
 
@@ -337,7 +337,7 @@
     ///
     /// Gives back the index of the given node.
     /// The lower bits of the integer describes the node.
-    int index(Node node) const {
+    static int index(Node node) {
       return Parent::index(node);
     }
 
diff --git a/lemon/smart_graph.h b/lemon/smart_graph.h
--- a/lemon/smart_graph.h
+++ b/lemon/smart_graph.h
@@ -508,7 +508,7 @@
       node._id = nodes.size() - 1;
     }
 
-    void next(Node& node) const {
+    static void next(Node& node) {
       --node._id;
     }
 
@@ -516,7 +516,7 @@
       arc._id = arcs.size() - 1;
     }
 
-    void next(Arc& arc) const {
+    static void next(Arc& arc) {
       --arc._id;
     }
 
@@ -524,7 +524,7 @@
       arc._id = arcs.size() / 2 - 1;
     }
 
-    void next(Edge& arc) const {
+    static void next(Edge& arc) {
       --arc._id;
     }
 
diff --git a/lemon/static_graph.h b/lemon/static_graph.h
--- a/lemon/static_graph.h
+++ b/lemon/static_graph.h
@@ -92,12 +92,12 @@
     void firstIn(Arc& e, const Node& n) const { e.id = node_first_in[n.id]; }
     void nextIn(Arc& e) const { e.id = arc_next_in[e.id]; }
 
-    int id(const Node& n) const { return n.id; }
-    Node nodeFromId(int id) const { return Node(id); }
+    static int id(const Node& n) { return n.id; }
+    static Node nodeFromId(int id) { return Node(id); }
     int maxNodeId() const { return node_num - 1; }
 
-    int id(const Arc& e) const { return e.id; }
-    Arc arcFromId(int id) const { return Arc(id); }
+    static int id(const Arc& e) { return e.id; }
+    static Arc arcFromId(int id) { return Arc(id); }
     int maxArcId() const { return arc_num - 1; }
 
     typedef True NodeNumTag;
@@ -268,25 +268,25 @@
     ///
     /// This function returns the node with the given index.
     /// \sa index()
-    Node node(int ix) const { return Parent::nodeFromId(ix); }
+    static Node node(int ix) { return Parent::nodeFromId(ix); }
 
     /// \brief The arc with the given index.
     ///
     /// This function returns the arc with the given index.
     /// \sa index()
-    Arc arc(int ix) const { return Parent::arcFromId(ix); }
+    static Arc arc(int ix) { return Parent::arcFromId(ix); }
 
     /// \brief The index of the given node.
     ///
     /// This function returns the index of the the given node.
     /// \sa node()
-    int index(Node node) const { return Parent::id(node); }
+    static int index(Node node) { return Parent::id(node); }
 
     /// \brief The index of the given arc.
     ///
     /// This function returns the index of the the given arc.
     /// \sa arc()
-    int index(Arc arc) const { return Parent::id(arc); }
+    static int index(Arc arc) { return Parent::id(arc); }
 
     /// \brief Number of nodes.
     ///