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What is an adjacency matrix?

Educative Answers Team

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.

svg viewer

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;
}

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matrix
adjacency
basics
graphs
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