Trying to understand Adjacency Matrix Representation of an Graph

Hi trying to understand toString method from the following code, It's clear to me that to represent graph in string format we 're iterating through vertex and array, but what's logic behind it? How it's exactly working? Any help would be appreciated
: public class AdjMatrixGraph {

private int V; // number of vertices in Graph
private int E; // number of edges in Graph
private int[][] adjMatrix;

public AdjMatrixGraph(int nodes) {
    this.V = nodes;
    this.E = 0;
    this.adjMatrix = new int[nodes][nodes];
}

public void addEdge(int u, int v) {
    adjMatrix[u][v] = 1;
    adjMatrix[v][u] = 1; // because it is an undirected graph
    E++;
}

public String toString() {
    StringBuilder sb = new StringBuilder();
    sb.append(V + " vertices, " + E + " edges " + "\n");
    for(int v = 0; v < V; v++) {
        sb.append(v + ": ");
        for(int w : adjMatrix[v]) {
            sb.append(w + " ");
        }
        sb.append("\n");
    }
    return sb.toString();
}

public static void main(String[] args) {
    AdjMatrixGraph g = new AdjMatrixGraph(4);
    g.addEdge(0, 1);
    g.addEdge(1, 2);
    g.addEdge(2, 3);
    g.addEdge(3, 0);
    System.out.println(g);
}

}