Implementation of BFS using adjacency matrix

Last Updated : 06 Jun, 2025

Breadth First Search (BFS) has been discussed in this article which uses adjacency list for the graph representation. In this article, adjacency matrix will be used to represent the graph.

Adjacency matrix representation: In adjacency matrix representation of a graph, the matrix mat[][] of size n*n (where n is the number of vertices) will represent the edges of the graph where mat[i][j] = 1 represents that there is an edge between the vertices i and j while mat[i][j] = 0 represents that there is no edge between the vertices i and j.

Implementation-of-BFS-using-adjacency-matrix-1

Below is the adjacency matrix representation of the graph shown in the above image:

0 1 2 3
0 0 1 1 0
1 1 0 0 1
2 1 0 0 0
3 0 1 0 0

Examples:

Input: source = 0

Output: 0 1 2 3

Input: source = 1

Output:1 0 2 3 4

Approach:

Create a matrix of size n*n where every element is 0 representing there is no edge in the graph.
Now, for every edge of the graph between the vertices i and j set mat[i][j] = 1.
After the adjacency matrix has been created and filled, find the BFS traversal of the graph as described in this post.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;

vector<vector<int>> adj;


// function to add edge to the graph
void addEdge(int x,int y)
{
    adj[x][y] = 1;
    adj[y][x] = 1;
}

// Function to perform BFS on the graph
void bfs(int start)
{
    // Visited vector to so that
    // a vertex is not visited more than once
    // Initializing the vector to false as no
    // vertex is visited at the beginning
    vector<bool> visited(adj.size(), false);
    vector<int> q;
    q.push_back(start);
 
    // Set source as visited
    visited[start] = true;
 
    int vis;
    while (!q.empty()) {
        vis = q[0];
 
        // Print the current node
        cout << vis << " ";
        q.erase(q.begin());
 
        // For every adjacent vertex to the current vertex
        for (int i = 0; i < adj[vis].size(); i++) {
            if (adj[vis][i] == 1 && (!visited[i])) {
 
                // Push the adjacent node to the queue
                q.push_back(i);
 
                // Set
                visited[i] = true;
            }
        }
    }
}
 
// Driver code
int main()
{
  // number of vertices
  int v = 5;


  // adjacency matrix
  adj= vector<vector<int>>(v,vector<int>(v,0));

  addEdge(0,1);
  addEdge(0,2);
  addEdge(1,3);
  
  // perform bfs on the graph
  bfs(0);
}

Java

// Java implementation of the approach
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

class GFG{

static class Graph
{
    
    // Number of vertex
    int v;

    // Number of edges
    int e;

    // Adjacency matrix
    int[][] adj;

    // Function to fill the empty
    // adjacency matrix
    Graph(int v, int e)
    {
        this.v = v;
        this.e = e;
        
        adj = new int[v][v];
        for(int row = 0; row < v; row++)
            Arrays.fill(adj[row], 0);
    }
    
    // Function to add an edge to the graph
    void addEdge(int start, int e) 
    {
        
        // Considering a bidirectional edge
        adj[start][e] = 1;
        adj[e][start] = 1;
    }

    // Function to perform BFS on the graph
    void BFS(int start) 
    {
        
        // Visited vector to so that
        // a vertex is not visited more than once
        // Initializing the vector to false as no
        // vertex is visited at the beginning
        boolean[] visited = new boolean[v];
        Arrays.fill(visited, false);
        List<Integer> q = new ArrayList<>();
        q.add(start);

        // Set source as visited
        visited[start] = true;

        int vis;
        while (!q.isEmpty())
        {
            vis = q.get(0);

            // Print the current node
            System.out.print(vis + " ");
            q.remove(q.get(0));

            // For every adjacent vertex to
            // the current vertex
            for(int i = 0; i < v; i++)
            {
                if (adj[vis][i] == 1 && (!visited[i]))
                {
                    
                    // Push the adjacent node to
                    // the queue
                    q.add(i);

                    // Set
                    visited[i] = true;
                }
            }
        }
    }
}

// Driver code
public static void main(String[] args)
{
    
    int v = 5, e = 4;

    // Create the graph
    Graph G = new Graph(v, e);
    G.addEdge(0, 1);
    G.addEdge(0, 2);
    G.addEdge(1, 3);

    G.BFS(0);
}
}

// This code is contributed by sanjeev2552

Python3

# Python3 implementation of the approach 
class Graph:
    
    adj = []

    # Function to fill empty adjacency matrix
    def __init__(self, v, e):
        
        self.v = v
        self.e = e
        Graph.adj = [[0 for i in range(v)] 
                        for j in range(v)]

    # Function to add an edge to the graph
    def addEdge(self, start, e):
        
        # Considering a bidirectional edge
        Graph.adj[start][e] = 1
        Graph.adj[e][start] = 1

    # Function to perform DFS on the graph
    def BFS(self, start):
        
        # Visited vector to so that a
        # vertex is not visited more than 
        # once Initializing the vector to 
        # false as no vertex is visited at
        # the beginning 
        visited = [False] * self.v
        q = [start]

        # Set source as visited
        visited[start] = True

        while q:
            vis = q[0]

            # Print current node
            print(vis, end = ' ')
            q.pop(0)
            
            # For every adjacent vertex to 
            # the current vertex
            for i in range(self.v):
                if (Graph.adj[vis][i] == 1 and 
                      (not visited[i])):
                          
                    # Push the adjacent node 
                    # in the queue
                    q.append(i)
                    
                    # set
                    visited[i] = True

# Driver code
v, e = 5, 4

# Create the graph
G = Graph(v, e)
G.addEdge(0, 1)
G.addEdge(0, 2)
G.addEdge(1, 3)

# Perform BFS
G.BFS(0)

# This code is contributed by ng24_7

// C# implementation of the approach
using System;
using System.Collections.Generic;

public class GFG{

  class Graph
  {

    // Number of vertex
    public int v;

    // Number of edges
    public int e;

    // Adjacency matrix
    public int[,] adj;

    // Function to fill the empty
    // adjacency matrix
    public Graph(int v, int e)
    {
      this.v = v;
      this.e = e;

      adj = new int[v,v];
      for(int row = 0; row < v; row++)
        for(int col = 0; col < v; col++)
          adj[row, col] = 0;
    }

    // Function to add an edge to the graph
    public void addEdge(int start, int e) 
    {

      // Considering a bidirectional edge
      adj[start, e] = 1;
      adj[e, start] = 1;
    }

    // Function to perform BFS on the graph
    public void BFS(int start) 
    {

      // Visited vector to so that
      // a vertex is not visited more than once
      // Initializing the vector to false as no
      // vertex is visited at the beginning
      bool[] visited = new bool[v];
      List<int> q = new List<int>();
      q.Add(start);

      // Set source as visited
      visited[start] = true;

      int vis;
      while (q.Count != 0)
      {
        vis = q[0];

        // Print the current node
        Console.Write(vis + " ");
        q.Remove(q[0]);

        // For every adjacent vertex to
        // the current vertex
        for(int i = 0; i < v; i++)
        {
          if (adj[vis,i] == 1 && (!visited[i]))
          {

            // Push the adjacent node to
            // the queue
            q.Add(i);

            // Set
            visited[i] = true;
          }
        }
      }
    }
  }

  // Driver code
  public static void Main(String[] args)
  {

    int v = 5, e = 4;

    // Create the graph
    Graph G = new Graph(v, e);
    G.addEdge(0, 1);
    G.addEdge(0, 2);
    G.addEdge(1, 3);

    G.BFS(0);
  }
}

// This code is contributed by shikhasingrajput

JavaScript

// JavaScript implementation of the approach
const adj = [];

// function to add edge to the graph
function addEdge(x, y) {
  adj[x][y] = 1;
  adj[y][x] = 1;
}

// Function to perform BFS on the graph
function bfs(start) {
  // Visited array to keep track of visited nodes
  // Initializing the array with all false values as no vertex 
 // is visited at the beginning
  const visited = Array(adj.length).fill(false);
  const q = [];
  q.push(start);

  // Set source as visited
  visited[start] = true;

  let vis;
  while (q.length >0) {
    vis = q.shift();

    // Print the current node
    console.log(vis + " ");

    // For every adjacent vertex to the current vertex
    for (let i = 0; i < adj[vis].length; i++) {
      if (adj[vis][i] === 1 && !visited[i]) {
        // Push the adjacent node to the queue
        q.push(i);

        // Set the adjacent node as visited
        visited[i] = true;
      }
    }
  }
}

// Driver code

  // number of vertices
  const v = 5;

  // adjacency matrix
  for (let i = 0; i < v; i++) {
    adj[i] = Array(v).fill(0);
  }

  addEdge(0, 1);
  addEdge(0, 2);
  addEdge(1, 3);

  // perform bfs on the graph
  bfs(0);

Output

0 1 2 3

Time Complexity: O(N*N)
Auxiliary Space: O(N)

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