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

From → ToPathsFrom → ToPathsFrom → ToPaths
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)}
1. All 58 paths were found by executing the Edge Gravity Algorithm with any k≥4 (k=4). The subset of shortest paths are indicated by **