Data Structures, Algorithms, & Applications in Java
Chapter 17, Exercise 21

Let a[n][n + 1] be the two-dimensional array used to store the adjacency matrix A of an n vertex graph. The diagonal entries of A are not stored in a. However, all diagonal elements of A are required to be zero. Elements A(i,j) with i < j are in the upper triangle of A and are stored in a[i-1][j-1]. Elements A(i,j) with i > j are in the lower triangle of A and are stored in a[i-2][j-1]. With these observations, the code for set and get takes the form given below. A test program and output appear in the files GraphAdjacencyMatrix.*. 
public class GraphAdjacencyMatrix
{
   // data members
   boolean [][] a;   // adjacency array

   // constructor
   public GraphAdjacencyMatrix(int theVertices)
   {
      // validate theVertices
      if (theVertices < 0)
         throw new IllegalArgumentException
                   ("number of vertices must be >= 0");
   
      a = new boolean [theVertices][theVertices + 1];
   }
   
   // methods
   /** throws IndexOutOfBoundsException when
     * either i or j is not between 1 and a.length */
   void checkIndex(int i, int j)
   {
      if (i < 1 || j < 1 || i >  a.length || j >  a.length)
         throw new IndexOutOfBoundsException
             ("i = " + i + "  j = " + j + " vertices = "
              + a.length);
   }

   /** return A(i,j) */
   public int get(int i, int j)
   {
      checkIndex(i, j);

      // diagonal entry is always zero
      if (i == j)
         return 0;
   
      // not a diagonal entry
      if (i < j)
         // upper triangle
         return (a[i-1][j-1]) ? 1 : 0;
      else
         // lower triangle
         return (a[i-2][j-1]) ? 1 : 0;
   }
   
   /** set A(i,j) = newValue */
   public void set(int i, int j, int newValue)
   {
      checkIndex(i, j);

      // validate newValue
      if (newValue < 0 || newValue > 1)
         throw new IllegalArgumentException
                   ("new value must be 0 or 1");
   
      // store newValue
      if (i < j)
         // upper triangle
         a[i-1][j-1] = (newValue == 1) ? true : false;
      else
         if (i > j)
            // lower triangle
            a[i-2][j-1] = (newValue == 1) ? true : false;
           else
              // diagonal entry
              if (newValue == 1)
                 throw new IllegalArgumentException
                           ("diagonal value must be 0");
   }
}