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Convert Adjacency Matrix to Adjacency List representation of Graph

  • Difficulty Level : Medium
  • Last Updated : 26 Nov, 2021

Prerequisite: Graph and its representations 
Given a adjacency matrix representation of a Graph. The task is to convert the given Adjacency Matrix to Adjacency List representation. 
Examples: 
 

Input: arr[][] = [ [0, 0, 1], [0, 0, 1], [1, 1, 0] ] 
Output: The adjacency list is: 
0 -> 2 
1 -> 2 
2 -> 0 -> 1
Input: arr[][] = [ [0, 1, 0, 0, 1], [1, 0, 1, 1, 1], [0, 1, 0, 1, 0], [0, 1, 1, 0, 1], [1, 1, 0, 1, 0] ] 
Output: The adjacency list is: 
0 -> 1 -> 4 
1 -> 0 -> 2 -> 3 -> 4 
2 -> 1 -> 3 
3 -> 1 -> 2 -> 4 
4 -> 0 -> 1 -> 3 
 

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Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Let the 2D array be adj[][], a slot adj[i][j] = 1 indicates that there is an edge from vertex i to vertex j.
Adjacency List: An array of lists is used. The size of the array is equal to the number of vertices. Let the array be array[]. An entry array[i] represents the list of vertices adjacent to the ith vertex.
To convert an adjacency matrix to the adjacency list. Create an array of lists and traverse the adjacency matrix. If for any cell (i, j) in the matrix “mat[i][j] = 1“, it means there is an edge from i to j, so insert j in the list at i-th position in the array of lists.
Below is the implementation of the above approach:
 

C++




#include<bits/stdc++.h>
using namespace std;
 
// CPP program to convert Adjacency matrix
// representation to Adjacency List
 
// converts from adjacency matrix to adjacency list
vector<vector<int>> convert( vector<vector<int>> a)
{
    vector<vector<int>> adjList(a.size());
    for (int i = 0; i < a.size(); i++)
    {
         
        for (int j = 0; j < a[i].size(); j++)
        {
            if (a[i][j] == 1)
            {
                adjList[i].push_back(j);
            }
        }
    }
    return adjList;
}
     
// Driver code
int main()
{
    vector<vector<int>> a;
    vector<int> p({0, 0, 1});
    vector<int> q({0, 0, 1});
    vector<int> r({1, 1, 0}); // adjacency matrix
    a.push_back(p);
    a.push_back(q);
    a.push_back(r);
    vector<vector<int>> AdjList = convert(a);
    cout<<"Adjacency List:"<<endl;
     
    // print the adjacency list
    for (int i = 0; i < AdjList.size(); i++)
    {
        cout << i;
        for(int j = 0; j < AdjList[i].size(); j++)
        {
            if(j == AdjList[i].size() - 1)
            {
                cout << " -> " << AdjList[i][j] << endl;
                break;
            }
            else
                cout << " -> " << AdjList[i][j];
        }
    }
}
 
// This code is contributed by Surendra_Gangwar

Java




// Java program to convert adjacency
// matrix representation to
// adjacency list
import java.util.*;
 
public class GFG {
 
    // Function to convert adjacency
    // list to adjacency matrix
    static ArrayList<ArrayList<Integer>> convert(int[][] a)
    {
        // no of vertices
        int l = a[0].length;
        ArrayList<ArrayList<Integer>> adjListArray
        = new ArrayList<ArrayList<Integer>>(l);
 
        // Create a new list for each
        // vertex such that adjacent
        // nodes can be stored
        for (int i = 0; i < l; i++) {
            adjListArray.add(new ArrayList<Integer>());
        }
         
        int i, j;
        for (i = 0; i < a[0].length; i++) {
            for (j = 0; j < a.length; j++) {
                if (a[i][j] == 1) {
                    adjListArray.get(i).add(j);
                }
            }
        }
         
        return adjListArray;
    }
     
    // Function to print the adjacency list
    static void printArrayList(ArrayList<ArrayList<Integer>>
                                                adjListArray)
    {
        // Print the adjacency list
        for (int v = 0; v < adjListArray.size(); v++) {
            System.out.print(v);
            for (Integer u : adjListArray.get(v)) {
                System.out.print(" -> " + u);
            }
            System.out.println();
        }
    }
     
    // Driver Code
    public static void main(String[] args)
    {
        // Given Adjacency Matrix
        int[][] a = { { 0, 0, 1 },
                    { 0, 0, 1 },
                    { 1, 1, 0 } };
 
        // function to convert adjacency
        // list to adjacency matrix
        ArrayList<ArrayList<Integer>> adjListArray = convert(a);
        System.out.println("Adjacency List: ");
 
        printArrayList(adjListArray);
    }
}

Python3




# Python 3 program to convert Adjacency matrix
# representation to Adjacency List
 
from collections import defaultdict
# converts from adjacency matrix to adjacency list
def convert(a):
    adjList = defaultdict(list)
    for i in range(len(a)):
        for j in range(len(a[i])):
                       if a[i][j]== 1:
                           adjList[i].append(j)
    return adjList
 
# driver code
a =[[0, 0, 1], [0, 0, 1], [1, 1, 0]] # adjacency matrix
AdjList = convert(a)
print("Adjacency List:")
# print the adjacency list
for i in AdjList:
    print(i, end ="")
    for j in AdjList[i]:
        print(" -> {}".format(j), end ="")
    print()
  
# This code is contributed by Muskan Kalra.

C#




// C# program to convert adjacency
// matrix representation to
// adjacency list
using System;
using System.Collections.Generic;
 
class GFG
{
 
    // Function to convert adjacency
    // list to adjacency matrix
    static List<List<int>> convert(int[,] a)
    {
        // no of vertices
        int l = a.GetLength(0);
        List<List<int>> adjListArray = new List<List<int>>(l);
        int i, j;
         
        // Create a new list for each
        // vertex such that adjacent
        // nodes can be stored
        for (i = 0; i < l; i++)
        {
            adjListArray.Add(new List<int>());
        }
 
         
        for (i = 0; i < a.GetLength(0); i++)
        {
            for (j = 0; j < a.GetLength(1); j++)
            {
                if (a[i,j] == 1)
                {
                    adjListArray[i].Add(j);
                }
            }
        }
 
        return adjListArray;
    }
 
    // Function to print the adjacency list
    static void printList(List<List<int>> adjListArray)
    {
         
        // Print the adjacency list
        for (int v = 0; v < adjListArray.Count; v++)
        {
            Console.Write(v);
            foreach (int u in adjListArray[v])
            {
                Console.Write(" -> " + u);
            }
            Console.WriteLine();
        }
    }
 
    // Driver Code
    public static void Main(String[] args)
    {
         
        // Given Adjacency Matrix
        int[,] a = { { 0, 0, 1 }, { 0, 0, 1 }, { 1, 1, 0 } };
 
        // function to convert adjacency
        // list to adjacency matrix
        List<List<int>> adjListArray = convert(a);
        Console.WriteLine("Adjacency List: ");
 
        printList(adjListArray);
    }
}
 
// This code is contributed by 29AjayKumar
Output: 
Adjacency List:
0 -> 2
1 -> 2
2 -> 0 -> 1

 

Time Complexity: O(N ^ 2).
Auxiliary Space: O(N ^ 2). 




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