Cloning of a LinkedList and a Binary Tree with random pointers has already been discussed. The idea behind cloning a graph is pretty much similar.

The idea is to do a BFS traversal of the graph and while visiting a node make a clone node of it (a copy of original node). If a node is encountered which is already visited then it already has a clone node.

**How to keep track of the visited/cloned nodes?**

A HashMap/Map is required in order to maintain all the nodes which have already been created.

*Key stores*: Reference/Address of original Node

*Value stores*: Reference/Address of cloned Node

A copy of all the graph nodes has been made, **how to connect clone nodes?**

While visiting the neighboring vertices of a node *u *get the corresponding cloned node for u , let’s call that *cloneNodeU *, now visit all the neighboring nodes for *u *and for each neighbor find the corresponding clone node(if not found create one) and then push into the neighboring vector of *cloneNodeU *node.

**How to verify if the cloned graph is a correct?**

Do a BFS traversal before and after the cloning of graph. In BFS traversal display the value of a node along with its address/reference.

Compare the order in which nodes are displayed, if the values are same but the address/reference is different for both the traversals than the cloned graph is correct.

## C++

`// A C++ program to Clone an Undirected Graph ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `struct` `GraphNode ` `{ ` ` ` `int` `val; ` ` ` ` ` `//A neighbour vector which contains addresses to ` ` ` `//all the neighbours of a GraphNode ` ` ` `vector<GraphNode*> neighbours; ` `}; ` ` ` `// A function which clones a Graph and ` `// returns the address to the cloned ` `// src node ` `GraphNode *cloneGraph(GraphNode *src) ` `{ ` ` ` `//A Map to keep track of all the ` ` ` `//nodes which have already been created ` ` ` `map<GraphNode*, GraphNode*> m; ` ` ` `queue<GraphNode*> q; ` ` ` ` ` `// Enqueue src node ` ` ` `q.push(src); ` ` ` `GraphNode *node; ` ` ` ` ` `// Make a clone Node ` ` ` `node = ` `new` `GraphNode(); ` ` ` `node->val = src->val; ` ` ` ` ` `// Put the clone node into the Map ` ` ` `m[src] = node; ` ` ` `while` `(!q.empty()) ` ` ` `{ ` ` ` `//Get the front node from the queue ` ` ` `//and then visit all its neighbours ` ` ` `GraphNode *u = q.front(); ` ` ` `q.pop(); ` ` ` `vector<GraphNode *> v = u->neighbours; ` ` ` `int` `n = v.size(); ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `// Check if this node has already been created ` ` ` `if` `(m[v[i]] == NULL) ` ` ` `{ ` ` ` `// If not then create a new Node and ` ` ` `// put into the HashMap ` ` ` `node = ` `new` `GraphNode(); ` ` ` `node->val = v[i]->val; ` ` ` `m[v[i]] = node; ` ` ` `q.push(v[i]); ` ` ` `} ` ` ` ` ` `// add these neighbours to the cloned graph node ` ` ` `m[u]->neighbours.push_back(m[v[i]]); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Return the address of cloned src Node ` ` ` `return` `m[src]; ` `} ` ` ` `// Build the desired graph ` `GraphNode *buildGraph() ` `{ ` ` ` `/* ` ` ` `Note : All the edges are Undirected ` ` ` `Given Graph: ` ` ` `1--2 ` ` ` `| | ` ` ` `4--3 ` ` ` `*/` ` ` `GraphNode *node1 = ` `new` `GraphNode(); ` ` ` `node1->val = 1; ` ` ` `GraphNode *node2 = ` `new` `GraphNode(); ` ` ` `node2->val = 2; ` ` ` `GraphNode *node3 = ` `new` `GraphNode(); ` ` ` `node3->val = 3; ` ` ` `GraphNode *node4 = ` `new` `GraphNode(); ` ` ` `node4->val = 4; ` ` ` `vector<GraphNode *> v; ` ` ` `v.push_back(node2); ` ` ` `v.push_back(node4); ` ` ` `node1->neighbours = v; ` ` ` `v.clear(); ` ` ` `v.push_back(node1); ` ` ` `v.push_back(node3); ` ` ` `node2->neighbours = v; ` ` ` `v.clear(); ` ` ` `v.push_back(node2); ` ` ` `v.push_back(node4); ` ` ` `node3->neighbours = v; ` ` ` `v.clear(); ` ` ` `v.push_back(node3); ` ` ` `v.push_back(node1); ` ` ` `node4->neighbours = v; ` ` ` `return` `node1; ` `} ` ` ` `// A simple bfs traversal of a graph to ` `// check for proper cloning of the graph ` `void` `bfs(GraphNode *src) ` `{ ` ` ` `map<GraphNode*, ` `bool` `> visit; ` ` ` `queue<GraphNode*> q; ` ` ` `q.push(src); ` ` ` `visit[src] = ` `true` `; ` ` ` `while` `(!q.empty()) ` ` ` `{ ` ` ` `GraphNode *u = q.front(); ` ` ` `cout << ` `"Value of Node "` `<< u->val << ` `"\n"` `; ` ` ` `cout << ` `"Address of Node "` `<<u << ` `"\n"` `; ` ` ` `q.pop(); ` ` ` `vector<GraphNode *> v = u->neighbours; ` ` ` `int` `n = v.size(); ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` `if` `(!visit[v[i]]) ` ` ` `{ ` ` ` `visit[v[i]] = ` `true` `; ` ` ` `q.push(v[i]); ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `cout << endl; ` `} ` ` ` `// Driver program to test above function ` `int` `main() ` `{ ` ` ` `GraphNode *src = buildGraph(); ` ` ` `cout << ` `"BFS Traversal before cloning\n"` `; ` ` ` `bfs(src); ` ` ` `GraphNode *newsrc = cloneGraph(src); ` ` ` `cout << ` `"BFS Traversal after cloning\n"` `; ` ` ` `bfs(newsrc); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to Clone an Undirected Graph ` `import` `java.util.*; ` ` ` `// GraphNode class represents each ` `// Node of the Graph ` `class` `GraphNode ` `{ ` ` ` `int` `val; ` ` ` ` ` `// A neighbour Vector which contains references to ` ` ` `// all the neighbours of a GraphNode ` ` ` `Vector<GraphNode> neighbours; ` ` ` `public` `GraphNode(` `int` `val) ` ` ` `{ ` ` ` `this` `.val = val; ` ` ` `neighbours = ` `new` `Vector<GraphNode>(); ` ` ` `} ` `} ` ` ` `class` `Graph ` `{ ` ` ` `// A method which clones the graph and ` ` ` `// returns the reference of new cloned source node ` ` ` `public` `GraphNode cloneGraph(GraphNode source) ` ` ` `{ ` ` ` `Queue<GraphNode> q = ` `new` `LinkedList<GraphNode>(); ` ` ` `q.add(source); ` ` ` ` ` `// An HashMap to keep track of all the ` ` ` `// nodes which have already been created ` ` ` `HashMap<GraphNode,GraphNode> hm = ` ` ` `new` `HashMap<GraphNode,GraphNode>(); ` ` ` ` ` `//Put the node into the HashMap ` ` ` `hm.put(source,` `new` `GraphNode(source.val)); ` ` ` ` ` `while` `(!q.isEmpty()) ` ` ` `{ ` ` ` `// Get the front node from the queue ` ` ` `// and then visit all its neighbours ` ` ` `GraphNode u = q.poll(); ` ` ` ` ` `// Get corresponding Cloned Graph Node ` ` ` `GraphNode cloneNodeU = hm.get(u); ` ` ` `if` `(u.neighbours != ` `null` `) ` ` ` `{ ` ` ` `Vector<GraphNode> v = u.neighbours; ` ` ` `for` `(GraphNode graphNode : v) ` ` ` `{ ` ` ` `// Get the corresponding cloned node ` ` ` `// If the node is not cloned then we will ` ` ` `// simply get a null ` ` ` `GraphNode cloneNodeG = hm.get(graphNode); ` ` ` ` ` `// Check if this node has already been created ` ` ` `if` `(cloneNodeG == ` `null` `) ` ` ` `{ ` ` ` `q.add(graphNode); ` ` ` ` ` `// If not then create a new Node and ` ` ` `// put into the HashMap ` ` ` `cloneNodeG = ` `new` `GraphNode(graphNode.val); ` ` ` `hm.put(graphNode,cloneNodeG); ` ` ` `} ` ` ` ` ` `// add the 'cloneNodeG' to neighbour ` ` ` `// vector of the cloneNodeG ` ` ` `cloneNodeU.neighbours.add(cloneNodeG); ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `// Return the reference of cloned source Node ` ` ` `return` `hm.get(source); ` ` ` `} ` ` ` ` ` `// Build the desired graph ` ` ` `public` `GraphNode buildGraph() ` ` ` `{ ` ` ` `/* ` ` ` `Note : All the edges are Undirected ` ` ` `Given Graph: ` ` ` `1--2 ` ` ` `| | ` ` ` `4--3 ` ` ` `*/` ` ` `GraphNode node1 = ` `new` `GraphNode(` `1` `); ` ` ` `GraphNode node2 = ` `new` `GraphNode(` `2` `); ` ` ` `GraphNode node3 = ` `new` `GraphNode(` `3` `); ` ` ` `GraphNode node4 = ` `new` `GraphNode(` `4` `); ` ` ` `Vector<GraphNode> v = ` `new` `Vector<GraphNode>(); ` ` ` `v.add(node2); ` ` ` `v.add(node4); ` ` ` `node1.neighbours = v; ` ` ` `v = ` `new` `Vector<GraphNode>(); ` ` ` `v.add(node1); ` ` ` `v.add(node3); ` ` ` `node2.neighbours = v; ` ` ` `v = ` `new` `Vector<GraphNode>(); ` ` ` `v.add(node2); ` ` ` `v.add(node4); ` ` ` `node3.neighbours = v; ` ` ` `v = ` `new` `Vector<GraphNode>(); ` ` ` `v.add(node3); ` ` ` `v.add(node1); ` ` ` `node4.neighbours = v; ` ` ` `return` `node1; ` ` ` `} ` ` ` ` ` `// BFS traversal of a graph to ` ` ` `// check if the cloned graph is correct ` ` ` `public` `void` `bfs(GraphNode source) ` ` ` `{ ` ` ` `Queue<GraphNode> q = ` `new` `LinkedList<GraphNode>(); ` ` ` `q.add(source); ` ` ` `HashMap<GraphNode,Boolean> visit = ` ` ` `new` `HashMap<GraphNode,Boolean>(); ` ` ` `visit.put(source,` `true` `); ` ` ` `while` `(!q.isEmpty()) ` ` ` `{ ` ` ` `GraphNode u = q.poll(); ` ` ` `System.out.println(` `"Value of Node "` `+ u.val); ` ` ` `System.out.println(` `"Address of Node "` `+ u); ` ` ` `if` `(u.neighbours != ` `null` `) ` ` ` `{ ` ` ` `Vector<GraphNode> v = u.neighbours; ` ` ` `for` `(GraphNode g : v) ` ` ` `{ ` ` ` `if` `(visit.get(g) == ` `null` `) ` ` ` `{ ` ` ` `q.add(g); ` ` ` `visit.put(g,` `true` `); ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `System.out.println(); ` ` ` `} ` `} ` ` ` `// Driver code ` `class` `Main ` `{ ` ` ` `public` `static` `void` `main(String args[]) ` ` ` `{ ` ` ` `Graph graph = ` `new` `Graph(); ` ` ` `GraphNode source = graph.buildGraph(); ` ` ` `System.out.println(` `"BFS traversal of a graph before cloning"` `); ` ` ` `graph.bfs(source); ` ` ` `GraphNode newSource = graph.cloneGraph(source); ` ` ` `System.out.println(` `"BFS traversal of a graph after cloning"` `); ` ` ` `graph.bfs(newSource); ` ` ` `} ` `} ` |

*chevron_right*

*filter_none*

Output in Java:

BFS traversal of a graph before cloning Value of Node 1 Address of Node GraphNode@15db9742 Value of Node 2 Address of Node GraphNode@6d06d69c Value of Node 4 Address of Node GraphNode@7852e922 Value of Node 3 Address of Node GraphNode@4e25154f BFS traversal of a graph after cloning Value of Node 1 Address of Node GraphNode@70dea4e Value of Node 2 Address of Node GraphNode@5c647e05 Value of Node 4 Address of Node GraphNode@33909752 Value of Node 3 Address of Node GraphNode@55f96302

Output in C++:

BFS Traversal before cloning Value of Node 1 Address of Node 0x24ccc20 Value of Node 2 Address of Node 0x24ccc50 Value of Node 4 Address of Node 0x24cccb0 Value of Node 3 Address of Node 0x24ccc80 BFS Traversal after cloning Value of Node 1 Address of Node 0x24cd030 Value of Node 2 Address of Node 0x24cd0e0 Value of Node 4 Address of Node 0x24cd170 Value of Node 3 Address of Node 0x24cd200

Clone an undirected graph with multiple connected components

This article is contributed by **Chirag Agarwal**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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