directed graph(complete/not)

#include<iostream>
#include<bits/stdc++.h>
using namespace std;

int main()
{
    int v,a,b,k=1;

    cout<<"Enter vertex Number  : ";
    cin>>v;
        list<int>matrix[v+1];

    while(a!=0 && b!=0)
    {
        cout<<"Edge:"<<k<<endl;
        cin>>a>>b;
        cout<<endl;
        if(a>v || b>v)
        {
            cout<<"Invalid input";
        }
        else{

            matrix[a].push_back(b);

        }
        k++;
    }

    int c=0;
    for(int i=1;i<v;i++)
    {
        if(matrix[i].size()!=v-1)
            {c=1;
            break;
            }
    }

        if(c==1)
        {
        cout<<"Not complete graph"<<endl;

        }
        else
        {
        cout<<"complete graph";
        }

}