diff --git a/include/CXXGraph/Graph/Algorithm/Dinic_impl.hpp b/include/CXXGraph/Graph/Algorithm/Dinic_impl.hpp
new file mode 100644
index 000000000..0e68e1496
--- /dev/null
+++ b/include/CXXGraph/Graph/Algorithm/Dinic_impl.hpp
@@ -0,0 +1,87 @@
+#include <iostream>
+#include <queue>
+#include <limits>
+#include <unordered_map>
+#include <vector>
+#include "Node_impl.h"
+#include "CXXGraph/Graph/Graph_decl.h"
+
+
+namespace CXXGraph {
+
+template <typename T>
+class Graph {
+private:
+    std::unordered_map<CXXGraph::id_t, Node<T>> nodes;
+    std::unordered_map<CXXGraph::id_t, std::unordered_map<CXXGraph::id_t, int>> capacities;
+    std::unordered_map<CXXGraph::id_t, std::unordered_map<CXXGraph::id_t, int>> flow;
+    
+    bool bfs(const CXXGraph::id_t& source, const CXXGraph::id_t& sink, std::unordered_map<CXXGraph::id_t, int>& distance) {
+        for (auto& pair : nodes) {
+            distance[pair.first] = -1;
+        }
+        distance[source] = 0;
+        
+        std::queue<CXXGraph::id_t> q;
+        q.push(source);
+        
+        while (!q.empty()) {
+            CXXGraph::id_t current = q.front();
+            q.pop();
+            for (auto& [neighbor_id, capacity] : capacities[current]) {
+                if (distance[neighbor_id] == -1 && flow[current][neighbor_id] < capacity) {
+                    distance[neighbor_id] = distance[current] + 1;
+                    q.push(neighbor_id);
+                }
+            }
+        }
+        
+        return distance[sink] != -1;
+    }
+    
+    int dfs(const CXXGraph::id_t& current, const CXXGraph::id_t& sink, int flow_value, std::unordered_map<CXXGraph::id_t, int>& distance) {
+        if (current == sink) {
+            return flow_value;
+        }
+        
+        for (auto& [neighbor_id, capacity] : capacities[current]) {
+            if (distance[neighbor_id] == distance[current] + 1 && flow[current][neighbor_id] < capacity) {
+                int new_flow = dfs(neighbor_id, sink, std::min(flow_value, capacity - flow[current][neighbor_id]), distance);
+                if (new_flow > 0) {
+                    flow[current][neighbor_id] += new_flow;
+                    flow[neighbor_id][current] -= new_flow;
+                    return new_flow;
+                }
+            }
+        }
+        
+        return 0;
+    }
+    
+public:
+    // Other graph methods...
+
+    // Function to add an edge with capacity
+    void addEdge(const std::string& from_id, const std::string& to_id, int capacity) {
+        capacities[from_id][to_id] = capacity;
+        flow[from_id][to_id] = 0;
+        // Assuming nodes are already added to the graph
+    }
+    
+    // Dinic's algorithm to find maximum flow
+    int dinicsAlgorithm(const CXXGraph::id_t& source, const CXXGraph::id_t& sink) {
+        int max_flow = 0;
+        std::unordered_map<CXXGraph::id_t, int> distance;
+        
+        while (bfs(source, sink, distance)) {
+            int path_flow = 0;
+            while ((path_flow = dfs(source, sink, std::numeric_limits<int>::max(), distance)) != 0) {
+                max_flow += path_flow;
+            }
+        }
+        
+        return max_flow;
+    }
+};
+
+} // namespace CXXGraph
diff --git a/include/CXXGraph/Graph/Algorithm/Krager_impl.hpp b/include/CXXGraph/Graph/Algorithm/Krager_impl.hpp
new file mode 100644
index 000000000..19f45988b
--- /dev/null
+++ b/include/CXXGraph/Graph/Algorithm/Krager_impl.hpp
@@ -0,0 +1,66 @@
+#include <iostream>
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+#include <random>
+#include "Node_impl.h"
+#include "CXXGraph/Graph/Graph_decl.h"
+
+
+namespace CXXGraph {
+
+template <typename T>
+class Graph {
+private:
+    std::unordered_map<CXXGraph::id_t, Node<T>> nodes;
+    std::unordered_map<CXXGraph::id_t, std::unordered_set<CXXGraph::id_t>> adjacency_list;
+
+public:
+    // Other graph methods...
+
+    // Function to add an edge between two nodes
+    void addEdge(const std::string& from_id, const std::string& to_id) {
+        adjacency_list[from_id].insert(to_id);
+        adjacency_list[to_id].insert(from_id);
+        // Assuming nodes are already added to the graph
+    }
+
+    // Krager's algorithm for graph partitioning
+    std::pair<std::unordered_set<CXXGraph::id_t>, std::unordered_set<CXXGraph::id_t>> kragersAlgorithm() {
+        // Initialize clusters
+        std::unordered_set<CXXGraph::id_t> cluster1;
+        std::unordered_set<CXXGraph::id_t> cluster2;
+        for (const auto& node_pair : nodes) {
+            cluster1.insert(node_pair.first);
+        }
+
+        // Perform Krager's algorithm
+        std::random_device rd;
+        std::mt19937 gen(rd());
+        while (cluster1.size() > 2) {
+            // Select a random edge
+            std::uniform_int_distribution<size_t> dist(0, adjacency_list.size() - 1);
+            size_t rand_index = dist(gen);
+            auto it = std::next(std::begin(adjacency_list), rand_index);
+            CXXGraph::id_t u = it->first;
+            auto& neighbors = it->second;
+            std::uniform_int_distribution<size_t> dist_neighbor(0, neighbors.size() - 1);
+            size_t rand_neighbor_index = dist_neighbor(gen);
+            auto neighbor_it = std::next(std::begin(neighbors), rand_neighbor_index);
+            CXXGraph::id_t v = *neighbor_it;
+
+            // Merge clusters if the vertices belong to different clusters
+            if (cluster1.count(u) && cluster1.count(v)) {
+                cluster1.erase(v);
+                cluster2.insert(v);
+            } else if (cluster2.count(u) && cluster1.count(v)) {
+                cluster1.erase(v);
+                cluster2.insert(v);
+            }
+        }
+
+        return {cluster1, cluster2};
+    }
+};
+
+} // namespace CXXGraph
diff --git a/include/CXXGraph/Node/Node_decl.h b/include/CXXGraph/Node/Node_decl.h
index 0618f605e..6ef1982a0 100644
--- a/include/CXXGraph/Node/Node_decl.h
+++ b/include/CXXGraph/Node/Node_decl.h
@@ -49,6 +49,7 @@ class Node {
   const std::string &getUserId() const;
   const T &getData() const;
   void setData(T &&new_data);
+  
   // operator
   bool operator==(const Node<T> &b) const;
   bool operator<(const Node<T> &b) const;
diff --git a/include/CXXGraph/Node/Node_impl.hpp b/include/CXXGraph/Node/Node_impl.hpp
index eb6905c2c..8015c9d0d 100644
--- a/include/CXXGraph/Node/Node_impl.hpp
+++ b/include/CXXGraph/Node/Node_impl.hpp
@@ -70,6 +70,18 @@ void Node<T>::setData(T &&new_data) {
   this->data = std::move(new_data);
 }
 
+ bool deleteNodeById(const std::string &id) {
+    auto it = std::find_if(nodes.begin(), nodes.end(), [&](const auto &pair) {
+      return pair.second.getUserId() == id;
+    });
+
+    if (it != nodes.end()) {
+      nodes.erase(it);
+      return true; // Node deleted successfully
+    }
+    return false; // Node not found
+  }
+
 // The data type T must have an overload of the equality operator
 template <typename T>
 bool Node<T>::operator==(const Node<T> &b) const {