Graph I         
-------         
     X1
     |
X4 - A -  X2    
     |
     X3

Pairs: 
X1,A
X2,A
X3,A
X4,A  

Graph II         
--------         
     X1             Y1
     |              |
X4 - A -  X2 - Y4 - A - Y2     
     |              |
     X3             Y3

Pairs: 
X1,A   Y1,A   X2,Y4
X2,A   Y2,A
X3,A   Y3,A
X4,A   Y4,A