In[2]   SymIndex[2,  dim_]  
Apply[  (Sort[List[##]]  &),  Array[  List,  Array[dim  &,  2]],  {2}  ]
SymIndex[2,  3]
SymIndex[2,  6]  
In[3] SymIndex[4]  =
Apply[  Flatten[  Sort[  Map[  Sort,  Partition[List[##],  2]]]]  &,
Array[  List,  Array[3  &,  4]],  {4}]
Algorithm 1