Graph Representation

Note : if no of edges is N & no of vertices is M then

if value of nodes are 0-indexed i.e 0,1,2,3,,,, then adjacency matrix and list are of size M+1,N+1 for matrix && N+1 for list

else if 1 based indexed then take M,N & N only

Adjacency Matrix (directed) (space is O(V²)

#include <iostream>
using namespace std;
bool A[100][100];
void initialize()
    {
        for(int i = 0;i < 10;++i)
            for(int j = 0;j < 10;++j)
                A[i][j] = false;
    }
int main()
    {
        int x, y, nodes, edges;
        initialize();       //Since there is no edge initially
        cin >> nodes;       //Number of nodes
        cin >> edges;       //Number of edges
        for(int i = 0;i < edges;++i)
        {
           cin >> x >> y;
           A[x][y] = true;
          //Mark the edges from vertex x to vertex y
       } 
     // EXAMPLE
if(A[3][4] == true)
          cout << “There is an edge between 3 and 4” << endl;
      else 
          cout << “There is no edge between 3 and 4” << endl;
      return 0;
    }

Adjacency List (directed) (space is O(V + 2*E)

#include<iostream >
#include < vector >
    using namespace std;
    vector <int> adj[10];     // array of vectors
// or use unordered_map<int, vector<int> > adj;
    int main()
    {
        int x, y, nodes, edges;
        cin >> nodes;       //Number of nodes
        cin >> edges;       //Number of edges
        for(int e= 0;e < edges;++e)
        {
            cin >> x >> y;
            adj[x].push_back(y);   //Insert y in adjacency list of x
         }
for(int v= 0;v < nodes;++v)
    {   
        cout << "Adjacency list of node " << v+1<< ": ";
        for(int j = 0;j < adj[v].size();++j)
        cout << adj[i][j] << " --> ";
         
        cout<<endl;
}
    }
    return 0;
    }

If there is weight n edges too then take array of vector<pair<int,int>> arr[ ]