diff --git a/algorithm/tarjan.h b/algorithm/tarjan.h
index 3a72da6..a78d58a 100644
--- a/algorithm/tarjan.h
+++ b/algorithm/tarjan.h
@@ -4,71 +4,80 @@
 #include "graph/graph.h"
 using namespace graph;
 
-#include <stack>
+#include <algorithm>
 #include <iostream>
 #include <ranges>
-#include <iterator>
-#include <algorithm>
+#include <stack>
 
-namespace algorithm {
+namespace algo {
 
 template<typename T>
 class Tarjan {
 public:
   Tarjan(Graph<T> G) : G(G) {}
 
-  void findSCC();
+  //
+  std::vector<std::vector<T>> run();
 
-  void strongConnect(Vertex<T>& v);
-
-  std::uint16_t index = 0;
-  std::stack<Vertex<T>> S;
+  //
+  void strongConnect(const T& v);
 private:
+  // Necessary info about vertices when running Tarjan's algorithm
+  struct Payload {
+    std::int16_t index = -1;
+    std::int16_t lowlink = -1;
+    bool onStack = false;
+  };
+
   Graph<T> G;
+  std::stack<T> S;
+  std::int16_t index = 0;
+  std::map<T, Payload> vp;
+  std::vector<std::vector<T>> SCCs;
 };
 
 template<typename T>
-void Tarjan<T>::strongConnect(Vertex<T>& v) {
-  v.index, v.lowlink = index++;
-  v.onStack = true;
+inline void Tarjan<T>::strongConnect(const T& v) {
+  vp[v].index = vp[v].lowlink = index++;
+  vp[v].onStack = true;
   S.push(v);
-
-  for (auto& w : v.edges) {
-    if (w.index == -1) {
-      // successor w has not yet been visited, recurse on it
+  
+  for (const auto& w : G.adjMatrix[v]) {
+    if (vp[w].index == -1) {
       strongConnect(w);
-      v.lowlink = std::min(v.lowlink, w.lowlink);
-    } else if (w.onStack) {
-      // successor w is in stack S and hence in the current SCC
-      // if w is not on stack, then (v, w) is an edge pointing to an SCC
-      // already found and must be ignored
-      v.lowlink = std::min(v.lowlink, w.index);
+      vp[v].lowlink = std::min(vp[v].lowlink, vp[w].lowlink);
+    } else if (vp[w].onStack) {
+      vp[v].lowlink = std::min(vp[v].lowlink, vp[w].index);
     }
   }
 
-  // if v is a root node, pop the stack and generate an SCC
-  if (v.lowlink = v.index) {
-    // start a new SCC
-    Vertex<T> w;
+  // If v is a root node, pop the stack and generate an SCC
+  if (vp[v].lowlink == vp[v].index) {
+    std::vector<T> SCC;
+    bool finished = false;
     do {
-      w = S.top();
+      const auto& w = S.top();
       S.pop();
-      // add w to current SCC
-
-    } while (w != v);
+      vp[w].onStack = false;
+      SCC.push_back(w);
+      finished = vp[w].index == vp[v].index;
+    } while (!finished);
+    SCCs.push_back(SCC);
   }
 }
 
 template<typename T>
-void Tarjan<T>::findSCC() {
+inline std::vector<std::vector<T>> Tarjan<T>::run() {
 
-  for (auto& vertex : G.vertices) {
-    if (vertex.index == -1) {
-      strongConnect(vertex);
+  for (const auto& v : G.vertices) {
+    if (vp[v].index == -1) {
+      strongConnect(v);
     }
   }
+
+  return SCCs;
 }
 
-} // namespace algorithm
+} // namespace algo
 
 #endif
\ No newline at end of file
diff --git a/graph/graph.h b/graph/graph.h
index a661953..cae2e89 100644
--- a/graph/graph.h
+++ b/graph/graph.h
@@ -1,12 +1,11 @@
 #ifndef GRAPH_H_
 #define GRAPH_H_
 
-#include "vertex.h"
-
 #include <map>
 #include <set>
-#include <vector>
 #include <utility>
+#include <vector>
+#include <iostream>
 
 namespace graph {
 
@@ -16,50 +15,44 @@ public:
   Graph() = default;
 
   // Add vertex v
-  void insert(Vertex<T>& v);
+  void insert(const T& v);
 
   // Add edge between v and u
-  void insert(Vertex<T> v, Vertex<T> u);
+  void insert(const T& v, const T& u);
 
   // Delete vertex v
-  void erase(Vertex<T>& v);
+  void erase(T& v);
   
   // Delete edge between v and u
-  void erase(Vertex<T>& v, Vertex<T>& u);
-
-  // Return true if v and u are connected
-  bool connected(const Vertex<T>& v, const Vertex<T>& u) const;
+  void erase(T& v, T& u);
 
   // Adjacency matrix representation
-  std::vector<Vertex<T>> vertices;
+  std::set<T> vertices;
+  std::map<T, std::vector<T>> adjMatrix;
 };
 
 template<typename T>
-inline void Graph<T>::insert(Vertex<T>& v) {
-  vertices.push_back(v);
+inline void Graph<T>::insert(const T& v) {
+  vertices.insert(v);
 }
 
 template<typename T>
-inline void Graph<T>::insert(Vertex<T> v, Vertex<T> u) {
-  v.edges.push_back(u);
-  vertices.push_back(v);
+inline void Graph<T>::insert(const T& v, const T& u) {
+  vertices.insert(v);
+  vertices.insert(u);
+  adjMatrix[v].push_back(u);
 }
 
 template<typename T>
-inline void Graph<T>::erase(Vertex<T>& v) {
+inline void Graph<T>::erase(T& v) {
   //
 }
 
 template<typename T>
-inline void Graph<T>::erase(Vertex<T>& v, Vertex<T>& u) {
+inline void Graph<T>::erase(T& v, T& u) {
   //
 }
 
-template<typename T>
-inline bool Graph<T>::connected(const Vertex<T>& v, const Vertex<T>& u) const {
-  return false;
-}
-
 } // namespace graph
 
 #endif
\ No newline at end of file
diff --git a/graph/vertex.h b/graph/vertex.h
deleted file mode 100644
index 9d447ee..0000000
--- a/graph/vertex.h
+++ /dev/null
@@ -1,36 +0,0 @@
-#ifndef VERTEX_H_
-#define VERTEX_H_
-
-#include <cstdint>
-#include <compare>
-#include <ostream>
-#include <vector>
-
-namespace graph {
-
-template<typename T>
-class Vertex {
-public:
-  Vertex() = default;
-  Vertex(T v) : v(v) {}
-  
-  T v;
-  std::uint16_t index = -1;
-  std::uint16_t lowlink = -1;
-  bool onStack = false;
-  std::vector<Vertex<T>> edges;
-
-  auto operator<=>(const Vertex&) const = default;
-
-  template<typename T>
-  friend inline std::ostream& operator<<(std::ostream& os, const Vertex<T>& v);
-};
-
-template<typename T>
-inline std::ostream& operator<<(std::ostream& os, const Vertex<T>& vout) {
-  return os << vout.v;
-}
-
-} // namespace graph
-
-#endif
\ No newline at end of file
diff --git a/test/algorithm_test.cc b/test/algorithm_test.cc
new file mode 100644
index 0000000..e36d5d1
--- /dev/null
+++ b/test/algorithm_test.cc
@@ -0,0 +1,73 @@
+#include <doctest/doctest.h>
+
+#include "graph/graph.h"
+using namespace graph;
+#include "algorithm/tarjan.h"
+
+TEST_SUITE("Algorithms") {
+
+  TEST_CASE("Tarjan T_1") {
+
+    Graph<std::uint16_t> G;
+    G.insert(1, 2);
+    G.insert(2, 4);
+    G.insert(2, 3);
+    G.insert(3, 5);
+    G.insert(4, 1);
+    G.insert(5, 7);
+    G.insert(5, 9);
+    G.insert(6, 8);
+    G.insert(7, 3);
+    G.insert(8, 9);
+    G.insert(9, 6);
+
+    REQUIRE_EQ(G.vertices.size(), 9);
+
+    algo::Tarjan<std::uint16_t> tarjan(G);
+    auto result = tarjan.run();
+    
+    std::sort(result.begin(), result.end());
+    std::for_each(result.begin(), result.end(), [&](std::vector<std::uint16_t>& row) {
+      std::sort(row.begin(), row.end());
+    });
+    
+    std::vector<std::vector<std::uint16_t>> expected{
+      {1, 2, 4},
+      {3, 5, 7},
+      {6, 8, 9}
+    };
+
+    CHECK_EQ(expected, result);
+  }
+
+  TEST_CASE("Tarjan T_2") {
+
+    Graph<std::uint16_t> G;
+    G.insert(1, 4);
+    G.insert(1, 2);
+    G.insert(2, 5);
+    G.insert(3, 1);
+    G.insert(4, 3);
+    G.insert(4, 6);
+    G.insert(5, 7);
+    G.insert(6, 3);
+    G.insert(7, 2);
+
+    REQUIRE_EQ(G.vertices.size(), 7);
+
+    algo::Tarjan<std::uint16_t> tarjan(G);
+    auto result = tarjan.run();
+
+    std::sort(result.begin(), result.end());
+    std::for_each(result.begin(), result.end(), [&](std::vector<std::uint16_t>& row) {
+      std::sort(row.begin(), row.end());
+    });
+    
+    std::vector<std::vector<std::uint16_t>> expected{
+      {1, 3, 4, 6},
+      {2, 5, 7}
+    };
+
+    CHECK_EQ(expected, result);
+  }
+}
\ No newline at end of file
diff --git a/test/graph_test.cc b/test/graph_test.cc
index 7720b65..0244e0a 100644
--- a/test/graph_test.cc
+++ b/test/graph_test.cc
@@ -2,33 +2,22 @@
 
 #include "graph/graph.h"
 using namespace graph;
-#include "algorithm/tarjan.h"
 
-#include <cstdint>
-#include <iostream>
+TEST_SUITE("Graph test.") {
 
-TEST_SUITE("Testing Graph.") {
-
-  TEST_CASE("Insert vertices/edges.") {
+  TEST_CASE("Insertion.") {
     Graph<std::uint16_t> G;
+    //G.insert(1);
+    //G.insert(1, 2);
+    //G.insert(1, 4);
+    //G.insert(1, 6);
+    //G.insert(2, 4);
+    //G.insert(2, 5);
+    //G.insert(3, 4);
+    //G.insert(3, 6);
+    //G.insert(4, 6);
+    //G.insert(5, 6);
 
-    G.insert(1, 2);
-    G.insert(1, 4);
-    G.insert(1, 6);
-    G.insert(2, 4);
-    G.insert(2, 5);
-    G.insert(3, 4);
-    G.insert(3, 6);
-    G.insert(4, 6);
-    G.insert(5, 6);
     
-    Vertex<std::uint16_t> v1(1);
-    Vertex<std::uint16_t> v2(3);
-    Vertex<std::uint16_t> v3(5);
-    algorithm::Tarjan<std::uint16_t> tarjan(G);
-    tarjan.findSCC();
-
-    // CHECK_EQ(G.connected(1, 5), true);
-
   }
 }
\ No newline at end of file