Connected Components in an undirected graph

Given an undirected graph, print all connected components line by line. For example consider the following graph.

We strongly recommend to minimize your browser and try this yourself first.

We have discussed algorithms for finding strongly connected components in directed graphs in following posts.
Kosaraju’s algorithm for strongly connected components.
Tarjan’s Algorithm to find Strongly Connected Components

Finding connected components for an undirected graph is an easier task. We simple need to do either BFS or DFS starting from every unvisited vertex, and we get all strongly connected components. Below are steps based on DFS.

1) Initialize all vertices as not visited.
2) Do following for every vertex 'v'.
       (a) If 'v' is not visited before, call DFSUtil(v)
       (b) Print new line character

DFSUtil(v)
1) Mark 'v' as visited.
2) Print 'v'
3) Do following for every adjacent 'u' of 'v'.
     If 'u' is not visited, then recursively call DFSUtil(u)

Below is the implementation of above algorithm.

C++

// C++ program to print connected components in 
// an undirected graph 
#include<iostream> 
#include <list> 
using namespace std; 
  
// Graph class represents a undirected graph 
// using adjacency list representation 
class Graph 
{ 
    int V;    // No. of vertices 
  
    // Pointer to an array containing adjacency lists 
    list<int> *adj; 
  
    // A function used by DFS 
    void DFSUtil(int v, bool visited[]); 
public: 
    Graph(int V);   // Constructor 
    void addEdge(int v, int w); 
    void connectedComponents(); 
}; 
  
// Method to print connected components in an 
// undirected graph 
void Graph::connectedComponents() 
{ 
    // Mark all the vertices as not visited 
    bool *visited = new bool[V]; 
    for(int v = 0; v < V; v++) 
        visited[v] = false; 
  
    for (int v=0; v<V; v++) 
    { 
        if (visited[v] == false) 
        { 
            // print all reachable vertices 
            // from v 
            DFSUtil(v, visited); 
  
            cout << "\n"; 
        } 
    } 
} 
  
void Graph::DFSUtil(int v, bool visited[]) 
{ 
    // Mark the current node as visited and print it 
    visited[v] = true; 
    cout << v << " "; 
  
    // Recur for all the vertices 
    // adjacent to this vertex 
    list<int>::iterator i; 
    for(i = adj[v].begin(); i != adj[v].end(); ++i) 
        if(!visited[*i]) 
            DFSUtil(*i, visited); 
} 
  
Graph::Graph(int V) 
{ 
    this->V = V; 
    adj = new list<int>[V]; 
} 
  
// method to add an undirected edge 
void Graph::addEdge(int v, int w) 
{ 
    adj[v].push_back(w); 
    adj[w].push_back(v); 
} 
  
// Drive program to test above 
int main() 
{ 
    // Create a graph given in the above diagram 
    Graph g(5); // 5 vertices numbered from 0 to 4 
    g.addEdge(1, 0); 
    g.addEdge(2, 3); 
    g.addEdge(3, 4); 
  
    cout << "Following are connected components \n"; 
    g.connectedComponents(); 
  
    return 0; 
} 

Java

// Java program to print connected components in  
// an undirected graph  
import java.util.LinkedList; 
class Graph { 
    // A user define class to represent a graph. 
    // A graph is an array of adjacency lists. 
    // Size of array will be V (number of vertices 
    // in graph) 
    int V; 
    LinkedList<Integer>[] adjListArray; 
      
    // constructor 
    Graph(int V) { 
        this.V = V; 
        // define the size of array as 
        // number of vertices 
        adjListArray = new LinkedList[V]; 
  
        // Create a new list for each vertex 
        // such that adjacent nodes can be stored 
  
        for(int i = 0; i < V ; i++){ 
            adjListArray[i] = new LinkedList<Integer>(); 
        } 
    } 
      
    // Adds an edge to an undirected graph 
    void addEdge( int src, int dest) { 
        // Add an edge from src to dest. 
        adjListArray[src].add(dest); 
  
        // Since graph is undirected, add an edge from dest 
        // to src also 
        adjListArray[dest].add(src); 
    } 
      
    void DFSUtil(int v, boolean[] visited) { 
        // Mark the current node as visited and print it 
        visited[v] = true; 
        System.out.print(v+" "); 
        // Recur for all the vertices 
        // adjacent to this vertex 
        for (int x : adjListArray[v]) { 
            if(!visited[x]) DFSUtil(x,visited); 
        } 
  
    } 
    void connectedComponents() { 
        // Mark all the vertices as not visited 
        boolean[] visited = new boolean[V]; 
        for(int v = 0; v < V; ++v) { 
            if(!visited[v]) { 
                // print all reachable vertices 
                // from v 
                DFSUtil(v,visited); 
                System.out.println(); 
            } 
        } 
    } 
      
      
    // Driver program to test above 
    public static void main(String[] args){ 
        // Create a graph given in the above diagram  
        Graph g = new Graph(5); // 5 vertices numbered from 0 to 4  
          
        g.addEdge(1, 0);  
        g.addEdge(2, 3);  
        g.addEdge(3, 4); 
        System.out.println("Following are connected components"); 
        g.connectedComponents(); 
    } 
}     

Python 3

# Python program to print connected  
# components in an undirected graph 
class Graph: 
      
    # init function to declare class variables 
    def __init__(self,V): 
        self.V = V 
        self.adj = [[] for i in range(V)] 
  
    def DFSUtil(self, temp, v, visited): 
  
        # Mark the current vertex as visited 
        visited[v] = True
  
        # Store the vertex to list 
        temp.append(v) 
  
        # Repeat for all vertices adjacent 
        # to this vertex v 
        for i in self.adj[v]: 
            if visited[i] == False: 
                  
                # Update the list 
                temp = self.DFSUtil(temp, i, visited) 
        return temp 
  
    # method to add an undirected edge 
    def addEdge(self, v, w): 
        self.adj[v].append(w) 
        self.adj[w].append(v) 
  
    # Method to retrieve connected components 
    # in an undirected graph 
    def connectedComponents(self): 
        visited = [] 
        cc = [] 
        for i in range(self.V): 
            visited.append(False) 
        for v in range(self.V): 
            if visited[v] == False: 
                temp = [] 
                cc.append(self.DFSUtil(temp, v, visited)) 
        return cc 
  
# Driver Code 
if __name__=="__main__": 
      
    # Create a graph given in the above diagram 
    # 5 vertices numbered from 0 to 4 
    g = Graph(5); 
    g.addEdge(1, 0) 
    g.addEdge(2, 3) 
    g.addEdge(3, 4) 
    cc = g.connectedComponents() 
    print("Following are connected components") 
    print(cc) 
  
# This code is contributed by Abhishek Valsan  

C#

// C# program to print connected components in  
// an undirected graph  
using System; 
using System.Collections.Generic;  
  
public class Graph  
{ 
    // A user define class to represent a graph. 
    // A graph is an array of adjacency lists. 
    // Size of array will be V (number of vertices 
    // in graph) 
    int V; 
    List<int>[] adjListArray; 
      
    // constructor 
    Graph(int V)  
    { 
        this.V = V; 
          
        // define the size of array as 
        // number of vertices 
        adjListArray = new List<int>[V]; 
  
        // Create a new list for each vertex 
        // such that adjacent nodes can be stored 
  
        for(int i = 0; i < V ; i++) 
        { 
            adjListArray[i] = new List<int>(); 
        } 
    } 
      
    // Adds an edge to an undirected graph 
    void addEdge( int src, int dest) 
    { 
        // Add an edge from src to dest. 
        adjListArray[src].Add(dest); 
  
        // Since graph is undirected, add an edge from dest 
        // to src also 
        adjListArray[dest].Add(src); 
    } 
      
    void DFSUtil(int v, bool[] visited)  
    { 
        // Mark the current node as visited and print it 
        visited[v] = true; 
        Console.Write(v+" "); 
          
        // Recur for all the vertices 
        // adjacent to this vertex 
        foreach (int x in adjListArray[v])  
        { 
            if(!visited[x]) DFSUtil(x,visited); 
        } 
  
    } 
    void connectedComponents()  
    { 
        // Mark all the vertices as not visited 
        bool[] visited = new bool[V]; 
        for(int v = 0; v < V; ++v)  
        { 
            if(!visited[v])  
            { 
                // print all reachable vertices 
                // from v 
                DFSUtil(v,visited); 
                Console.WriteLine(); 
            } 
        } 
    } 
      
      
    // Driver code 
    public static void Main(String[] args) 
    { 
        // Create a graph given in the above diagram  
        Graph g = new Graph(5); // 5 vertices numbered from 0 to 4  
          
        g.addEdge(1, 0);  
        g.addEdge(2, 3);  
        g.addEdge(3, 4); 
        Console.WriteLine("Following are connected components"); 
        g.connectedComponents(); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Output:

0 1
2 3 4

Time complexity of above solution is O(V + E) as it does simple DFS for given graph.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

My Personal Notes

C++

Java

Python 3

C#

Recommended Posts: