diff --git a/algorithm/italiano.h b/algorithm/italiano.h
index 89fa9d8..1413789 100644
--- a/algorithm/italiano.h
+++ b/algorithm/italiano.h
@@ -52,6 +52,33 @@ bool Italiano<T>::query(const T& u, const T& v) {
 
 template<typename T>
 void Italiano<T>::remove(const T& u, const T& v) {
+  
+  for (const auto& w : G.adjMatrix) {
+    // Check if (u,v) edge of T(w) || p(w,v) points to (u,v)
+
+    // If yes => set p(w, v) to point to the next edge (u',v) in Ein(v)
+    // If (u,v) the last edge, then set it to point to null
+
+    // If T(w) contains u' then the new edge reconnects v to T(w)
+    // As this needs to be checked, we set R(w) <- {v}
+
+    // If (u,v) is not edge of T(w) or is the last edge in Ein(v), R(w) <- phi
+
+    // Remove (u,v) from Eout(u) and Ein(v)
+  }
+
+  for (const auto& w : G.adjMatrix) {
+
+    // Check tentative pointers of the vertices in R(w).
+    // While there is a vertex x in R(w), scan the edges in Ein(x), starting
+    // from the edge pointed to by p(w,x), until an edge (u',x) for which
+    // p(w,u') != null is found or Ein(x) is exhausted.
+
+    // If such edge is found, x is removed from R(w).
+    // If the list is exhausted, set p(w,x) to null and M(w,x) to 0
+
+    // Then scan all Eout(x). If (x,x') is tree edge, add x' to R(w)
+  }
 
 }
 
diff --git a/graph/graph.h b/graph/graph.h
index 7e2bae6..5f66243 100644
--- a/graph/graph.h
+++ b/graph/graph.h
@@ -45,6 +45,8 @@ Graph<T>::~Graph() {
 template<typename T>
 inline void Graph<T>::insert(const T& u, const T& v) {
   Graph<T>::adjMatrix[u].insert(v);
+  Graph<T>::adjMatrix[v];
+
 }
 
 template<typename T>
diff --git a/test/graph_test.cc b/test/graph_test.cc
index 8365ea7..e6d957d 100644
--- a/test/graph_test.cc
+++ b/test/graph_test.cc
@@ -45,13 +45,13 @@ TEST_SUITE("Graph") {
     CHECK_EQ(R, X);
   }
 
-  TEST_CASE("Digraph::V and Digraph::E") {
+  TEST_CASE("Graph::V and Graph::E") {
     // 1 --> 2 --> 3 --> 1
     //             3 --> 4 --> 5 --> 3
     //       2 --> 6 --> 7 --> 8 --> 6
     //             6 --> 9 --> 10 --> 11 --> 12 --> 13 --> 9
     //                                       12 --> 10
-    Digraph<std::uint16_t> G;
+    Graph<std::uint16_t> G;
     G.insert(1, 2);
     G.insert(2, 3);
     G.insert(3, 1);