An **adjacency matrix** is a two-dimensional matrix used to map the association between the nodes of a graph. A **graph** is a set of vertices (nodes) connected by edges.

> In an adjacency matrix, `0` means that no association between nodes exists and `1` means that an association between nodes does exist.

# Code
In the example below, we have implemented the adjacency matrix for the above illustration. 

> In a two-dimensional matrix, rows and columns are initialized with index `0` and so on. That's why we have subtracted `1` from each index below.

#include <iostream>
using namespace std;

int main() {
  int adjMatrix[5][5];

  // intializing adjMatrix to zero
  for(int i = 0; i < 5 ; i++){
    for(int j = 0; j < 5; j++){
      adjMatrix[i][j] = 0;
    }
  }

  // setting node 1
  adjMatrix[1-1][2-1] = 1;
  adjMatrix[1-1][3-1] = 1; 

  // setting node 2
  adjMatrix[2-1][1-1] = 1;
  adjMatrix[2-1][5-1] = 1;

  // setting node 3
  adjMatrix[3-1][1-1] = 1;
  adjMatrix[3-1][4-1] = 1; 

  // setting node 4
  adjMatrix[4-1][3-1] = 1;
  adjMatrix[4-1][5-1] = 1; 
  
  // setting node 5
  adjMatrix[5-1][2-1] = 1;
  adjMatrix[5-1][4-1] = 1; 


  // printing
  for(int i = 0; i < 5 ; i++){
    for(int j = 0; j < 5; j++){
      cout<< adjMatrix[i][j]<< " ";
    }
    cout<<"\n";
  }  
  return 0;
}

class AdjacencyMatrix {
    static int adjMatrix[][] = new int [5][5];

    public static void main( String args[] ) {
        
        // intialising to zero
        for(int i = 0; i < 5 ; i++){
            for(int j = 0; j < 5; j++){
                adjMatrix[i][j] = 0;
            }
        }    

        // setting node 1
        adjMatrix[1-1][2-1] = 1;
        adjMatrix[1-1][3-1] = 1; 

        // setting node 2
        adjMatrix[2-1][1-1] = 1;
        adjMatrix[2-1][5-1] = 1;

        // setting node 3
        adjMatrix[3-1][1-1] = 1;
        adjMatrix[3-1][4-1] = 1; 

        // setting node 4
        adjMatrix[4-1][3-1] = 1;
        adjMatrix[4-1][5-1] = 1; 
        
        // setting node 5
        adjMatrix[5-1][2-1] = 1;
        adjMatrix[5-1][4-1] = 1; 

        // printing
        for(int i = 0; i < 5 ; i++){
            for(int j = 0; j < 5; j++){
                System.out.print(adjMatrix[i][j]);
            }
            System.out.println("");
        }
    }
}

Java

# 5 x 5 two-dimensional matrix intialized to zero
adjMatrix = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]

# setting node 1
adjMatrix[1-1][2-1] = 1;
adjMatrix[1-1][3-1] = 1; 

# setting node 2
adjMatrix[2-1][1-1] = 1;
adjMatrix[2-1][5-1] = 1;

# setting node 3
adjMatrix[3-1][1-1] = 1;
adjMatrix[3-1][4-1] = 1; 

# setting node 4
adjMatrix[4-1][3-1] = 1;
adjMatrix[4-1][5-1] = 1; 
        
# setting node 5
adjMatrix[5-1][2-1] = 1;
adjMatrix[5-1][4-1] = 1;

# printing
for i in range(len(adjMatrix)):
    for j in range(len(adjMatrix[i])):
        print(adjMatrix[i][j], end=' ')
    print()

Python

What is an adjacency matrix?

An adjacency matrix is a two-dimensional matrix used to map the association between the nodes of a graph. A graph is a set of vertices (nodes) connected by edges.  In an adjacency matrix, 0 means that no association between nodes exists and 1 means that an association between nodes does exist.  