Table 2 Path enumeration for the small example in Fig. 1

1→2

{(1,2)}**

2→4

{(2,4)}**

4→2

{(4,2)}**

1→2

{(1,3),(3,2)}

2→4

{(2,3),(3,4)}

4→2

{(4,3),(3,2)}

1→2

{(1,3),(3,4),(4,2)}

2→4

{(2,1),(1,3),(3,4)}

4→2

{(4,3),(3,1),(1,2)}

1→3

{(1,3)}**

2→5

{(2,3),(3,5)}**

4→3

{(4,3)}**

1→3

{(1,2),(2,3)}

2→5

{(2,1),(1,3),(3,5)}

4→3

{(4,2),(2,3)}

1→3

{(1,2),(2,4),(4,3)}

2→5

{(2,4),(4,3),(3,5)}

4→3

{(4,2),(2,1),(1,3)}

1→4

{(1,2),(2,4)}**

3→1

{(3,1)}**

4→5

{(4,3),(3,5)}**

1→4

{(1,3),(3,4)}**

3→1

{(3,2),(2,1)}

4→5

{(4,2),(2,3),(3,5)}

1→4

{(1,3),(3,2),(2,4)}

3→1

{(3,4),(4,2),(2,1)}

4→5

{(4,2),(2,1),(1,3),(3,5)}

1→4

{(1,2),(2,3),(3,4)}

1→5

{(1,3),(3,5)}**

3→2

{(3,2)}**

5→1

{(5,3),(3,1)}**

1→5

{(1,2),(2,3),(3,5)}

3→2

{(3,1),(1,2)}

5→1

{(5,3),(3,2),(2,1)}

1→5

{(1,2),(2,4),(4,3),(3,5)}

3→2

{(3,4),(4,2)}

5→1

{(5,3),(3,4),(4,2),(2,1)}

2→1

{(2,1)}**

3→4

{(3,4)}**

5→2

{(5,3),(3,2)}**

2→1

{(2,3),(3,1)}

3→4

{(3,2),(2,4)}

5→2

{(5,3),(3,1),(1,2)}

2→1

{(2,4),(4,3),(3,1)}

3→4

{(3,1),(1,2),(2,4)}

5→2

{(5,3),(3,4),(4,2)}

3→5

{(3,5)}**

5→3

{(5,3)}**

2→3

{(2,3)}**

4→1

{(4,2),(2,1)}**

5→4

{(5,3),(3,4)}**

2→3

{(2,1),(1,3)}

4→1

{(4,3),(3,1)}**

5→4

{(5,3),(3,2),(2,4)}

2→3

{(2,4),(4,3)}

4→1

{(4,3),(3,2),(2,1)}

5→4

{(5,3),(3,1),(1,2),(2,4)}

4→1

{(4,2),(2,3),(3,1)}