Matrix of Figure 4(a)

     [0211]
     [2101]
M =  [1000]
     [1100]

Table 1

---------------------------------------------------------------
| Vertex | # of edges  | # of edges | # of paths with vertex  |
| v_i    |  v_1 to v_i | v_i to v_2 | sequence v_1 v_i v_2    |
---------------------------------------------------------------
|  v_1   | M[1,1] = 0  | M[1,2] = 2 | M[1,1]*M[1,2] = 0*2 = 0 |
|  v_2   | M[1,2] = 2  | M[2,2] = 1 | M[1,2]*M[2,2] = 2*1 = 2 |
|  v_3   | M[1,3] = 1  | M[3,2] = 0 | M[1,3]*M[3,2] = 1*0 = 0 |
|  v_4   | M[1,4] = 1  | M[4,2] = 1 | M[1,4]*M[4,2] = 1*1 = 1 |
---------------------------------------------------------------