Table 2.

An enumeration of the connectible pairs for the graph in Figure 1.

Distinct separator S	ms	Variables in cliques of components of Fs	Sizes	α (S)
∅	4	{4} {6} {13, 14, 15, 23}	1, 1, 4, 17	111
		{1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 21, 22}
{13, 14}	1	{15} {23}	1,1	1
{3}	3	{20} {5} {7, 17, 22} {1, 2, 16, 18, 19}	1, 1, 3, 5	32
{2,3}	2	{1} {16} {18}	1,1,1	3
{3,18}	1	{2} {19}	1, 1	1
{9}	1	{10} {12, 17}	1,2	2
{12}	1	{11} {9, 17}	1,2	2
{17}	3	{8} {21} {9, 12} {3, 7, 22}	1, 1, 2, 3	17

Total number of connectible pairs 169