2D Object Array Memory Issues C++

When my input looks like this:

11

Harry Kate Fred Carol

My adjacency matrix should put Harry at [7][7], Kate at [7][10], Fred at [7][5], and Carol at [7][2]. However, Carol & Kate get inserted at other locations within the adj. matrix as well. I am guessing this has something to do with stack and heap memory, but I am not sure how to find the bug. Using cout statements, there doesn't appear to be any issues.

Code below

#include <iostream>
#include <string>
#include <stdlib.h>
#include <iostream>
#include <sstream>
using namespace std;

class Element {

public:
    string name;
    int weight;
    string color;

    //default constructor
    Element(void) {
        name = "";
        weight = 0;
        color = "white";
    }

    //parameterized constructor
    Element(string first) {
        name = first;
        weight = 0;
        color = "white";
    }

    void setBlack() {
        color = "black";
    }
};

class AdjMatrix {

public:
    int size;
    Element ***adj_matrix;
    AdjMatrix(void) {
        size = 0;
        adj_matrix = NULL;
    }

    AdjMatrix(int n) {
        size = n; //sets the size to n
        adj_matrix = new Element **[size];
        for (int i = 0; i < size; i++) {
            adj_matrix[i] = new Element *[i];
        }
    }

    //Destructor class
    ~AdjMatrix(void) {
        delete adj_matrix;
        adj_matrix = NULL;
    }

    //initialize the array with empty elements
    void initialize_matrix() {
        Element *add_element = new Element("");
        for (int i = 0; i < size; i++) {
            for (int j = 0; j < size; j++)
                adj_matrix[i][j] = add_element;
        }
    }
};


int convertToASCII(string letter)
{
   int x = letter.at(0);
   int index = x - 65;
    return index;
};

int main(int argc, char *argv[]) {

    string table_size;
    cout<<"";
    getline(cin,table_size);
    int size = atoi(table_size.c_str());
    AdjMatrix *myGraph = new AdjMatrix(size);
    myGraph->initialize_matrix();

string line;
getline(cin, line);
while (getline(cin,line))
{
    if (line.empty())
        break;

    else {

        int x = convertToASCII(line);
        stringstream linestream(line);
        string temp;

        while (linestream >> temp) {
            int z = convertToASCII(temp);
            myGraph->adj_matrix[x][z] = new Element(temp);
        }
    }
}

//Print graph
for (int i = 0; i < myGraph->size; i++) {
    for (int j = 0; j < myGraph->size; j++)
        cout<<"["<<i<<"]["<<j<<"]: "<<myGraph->adj_matrix[i][j]->name<<endl;
}

  return 0;
}