verificare de graf hamiltonian

#include<iostream>
#include<fstream>
#include<vector>
typedef std::vector<std::vector<int>> matrix;
matrix g;
int n, m;  //no of vertices and edges

void read()
{
    std::ifstream in("file.txt");
    if (in.is_open())
    {
        in >> n >> m;
        //init a nxn matrix with 0
        g.resize(n);
        for (int i = 0; i < n; i++)
            g[i].assign(n, 0);
        int x, y;
        for (int i = 0; i < m; i++)
        {
            in>> x >> y;
            g[x][y] = 1;
            g[y][x] = 1;
        }
    }
    else
        std::cout << "Unable to open the file!\n";
}

int is_hamiltonian()
{
    if (n < 3)
        return 0;
    int grade = 0;
    for (int i = 0; i < n; i++)
    {
        grade = 0;
        for (int j = 0; j < n; j++)
            if (g[i][j] == 1)
                grade++;
        if (grade < n / 2)
            return 0;
    }
    return 1;
}
int main()
{
    read();
    if (is_hamiltonian())
        std::cout << "Is hamiltonian\n";
    else
        std::cout << "Isn't hamiltonian\n";
    return 0;
}

/*
6
11
0 1
0 4
0 5
1 2
1 4
2 3
2 4
3 4
4 5
1 5
1 3

*/