Objects pointed in a vector of pointers cannot be accessed - I don't understand why

Question

Thanks to anyone who will help me with this. I am quite new to C++ and I am doing my best to learn the basics of memory and pointers.

In the following code, my goal is to create a vector of pointers to Objects of class "Node" (each with its own integer value), and to create a class "Graph" which essentially is a pointer to the vector itself and a method to print the integer value of the first node.

To create the vector, I use a function "generate_vec_nodes" (inserted in the Constructor of the "Graph" class) that:

1. allocates memory in the heap for the vector
2. allocates memory in the heap for each new node
3. push_back the new node's pointer in the vector
4. return the vector's pointer to the Constructor of the Graph Class, that creates a Graph Object.

My problem is: when it is time to retrieve the integer value of the first node, in the "test" function called in Main, I get a Segmentation Fault. It looks like the memory cannot be accessed. I tried to access the element with "(*P_nodes_vec)[0]" inside the Graph Constructor, just after it is returned after being created, and I can do that.

To me it looks like one between the vector Object or the Node Object is deleted or cannot be accessed, but I really do not understand why. I am creating them in the Heap (so they should not be destroyed), and they should be always accessible by the Graph Class method "test" and/or by the Node Class method "get_node_integer" because the Graph Class is a friend class of Node.

The code is:

#include <iostream>
#include <vector>


class node
{
    public:
        friend class graph;
        
        // constructor:
        node(void){int node_integer = 1;};

        // function to set the node_to:
        void set_node_integer(int x){node_integer = x;};

        // function to get the node_to:
        int get_node_integer(){return node_integer;};

    //private:
        int node_integer;

};

///////////////////////////

// function to generate a vector of pointers to nodes, and to return a pointer to this vector:

std::vector<node*> * generate_vec_nodes() 
{
        std::vector<node*> * new_P_nodes_vec = new std::vector<node*>;

        for(int i = 0 ; i < 169 ; i++)
        {
            node* next_node = new node();
            next_node->set_node_integer(i);
            new_P_nodes_vec->push_back(next_node);
        };

        return new_P_nodes_vec;
};

////////////////////////////

class graph
{
    private:
        
        // vector of nodes:
        std::vector<node*> * P_nodes_vec;

    public:

        // constructor:
        graph()
        {

            // create a pointer to a vector of 169 nodes:
            std::vector<node*> * P_nodes_vec = generate_vec_nodes();

        };

        // "test" method:

        void test(void)
        {
            std::cout << "Hello 1" << std::endl;
            std::cout << (*P_nodes_vec)[0]->get_node_integer() << std::endl;
            std::cout << "Hello 2" << std::endl;
        };
};

////////////////////////////

int main()

{

    // generate the graph:
    graph my_graph = graph();

    std::cout << std::endl;
    std::cout << std::endl;
    
    my_graph.test();

    std::cout << std::endl;
    std::cout << std::endl;

    std::cout << "End of computations";

    std::cout << std::endl;
    std::cout << std::endl;

    return 0;

};