Create a Graph of nodes from an adjacency matrix C++

[SeanBlack0000]

I am trying to create a graph from a 2d matrix of booleans. When the index [i][j] == 1, I need to create a link or edge from node[i] to node[j]. I am doing some thing wrong. I have created a class file with a struct node and some basic operations. I have realized a pointer of the struct in not the correct way to go about this. A node may have more than one edge to other nodes, and one pointer is not going to link them. Please help a struggling programming student. My code and output is listed below.

//LinkNode.h

#ifndef LINKNODE_H
#define LINKNODE_H

#include <string>
#include <iostream>
using namespace std;

class LinkNode
{
private:
    typedef struct Node
    {
            string msg;
            int data;
            Node * next_node;

    } * nodePtr; 
        nodePtr root;
        nodePtr newNode;
        nodePtr head;       
        nodePtr tempPtr;
public:
    LinkNode();
    void addNode(int addData);
    void printList();
};
#endif




//LinkNode.cpp

#include "LinkNode.h"
#include <iostream>
#include <cstdlib>
using namespace std;

LinkNode::LinkNode()
{
    head = tempPtr = root = NULL;
    //next_node = NULL;
}

void LinkNode::addNode(int addData)
{
        if(root == NULL)
        {
                root = new Node;
                root->next_node = NULL;
                root->data = addData;
        }

        else 
        {
                tempPtr = root;                         //   temp variable ptr
                while(tempPtr->next_node != NULL)       //find the last node
                        tempPtr = tempPtr->next_node;       //in the linked list

                newNode = new Node();
                newNode->data = addData;
                newNode->next_node = NULL;              
                tempPtr->next_node = newNode;
        }

}

void LinkNode::printList()
{
    tempPtr = root;
    while(tempPtr != NULL)
    {
        cout << tempPtr->data << endl;  
        tempPtr = tempPtr->next_node;
    }
}


//main.cpp

/*////////////////////////////////////////////////////////////////////
//                                                                  //
//  (N0)    0-------------------0\  (N1)                            //
//          |                 / |   \                               //
//          |               /   |      \                            //
//          |             /     |         \                         //
//          |           /       |           \                       //
//          |         /         |             0  (N2)               //
//          |       /           |           /                       //
//          |     /             |         /                         //
//          |   /               |      /                            //
//          | /                 |   /                               //
//  (N4)    0-------------------0/  (N3)                            //
//                                                                  //
//  N = Nodes                                                       //
//  The adjacency matrix for the graph is listed below.             //
*/////////////////////////////////////////////////////////////////////



#include <iostream>
#include <array>
#include <string>
#include <vector>
#include <cstdlib>
#include <ctime>
#include <exception>
#include "Stack.h"
#include "LinkNode.h"

using namespace std;
const int adjmatrix[5][5] = {
  {0,1,0,0,1},
  {1,0,1,1,1},
  {0,1,0,1,0},
  {0,1,1,0,1},
  {1,1,0,1,0},
};

// create nodes
    LinkNode Graph;
    for(int i=0; i<5; i++)
        for(int j=0; j<5; j++)
        {
            if(adjmatrix[i][j] == 1) 
            {
                Graph.addNode(i);
                Graph.printList();  

            }

        }  
  cout << endl << endl << endl;
 system("pause");
  return 0;
}


// output 

0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
1
2
2
0
0
1
1
1
1
2
2
3
0
0
1
1
1
1
2
2
3
3
0
0
1
1
1
1
2
2
3
3
3
0
0
1
1
1
1
2
2
3
3
3
4
0
0
1
1
1
1
2
2
3
3
3
4
4
0
0
1
1
1
1
2
2
3
3
3
4
4
4