Spanning Run

R

[2, 3, 1, 2]

B

[4, 4, 4, 3]

pi

[3, 5, 6, 7]

indegrees

[1, 2, 2, 3]

Friedman weight

21

det

17/64, .2656250000

nullspace of Delta

{1, 2, 3, 4}

nullspace of A

` det(A) = ` -1/8

spanNum

21

Data

Coloring	R-cycles	B-cycles	Sync'd/Not Sync'd	R/B/Delta Ranking
1. {}	{{1, 2, 3}}	{{3, 4}}	syncd, [2, 3, 1, 2], [4, 4, 4, 3]	3:3 , 2:2 , 3:3
2. {2}	{{2, 4}}	{{3, 4}}	syncd, [2, 4, 1, 2], [4, 3, 4, 3]	2:2 , 2:2 , 3:3
3. {3}	{{2, 3, 4}}	{{1, 3, 4}}	syncd, [2, 3, 4, 2], [4, 4, 1, 3]	3:3 , 3:3 , 3:3
4. {4}	{{1, 2, 3}}	{{2, 4}}	syncd, [2, 3, 1, 3], [4, 4, 4, 2]	3:3 , 2:2 , 3:3
5. {2, 3}	{{2, 4}}	{{1, 3, 4}}	syncd, [2, 4, 4, 2], [4, 3, 1, 3]	2:2 , 3:3 , 3:3
6. {2, 4}	{{1, 2, 3, 4}}	{{2, 3, 4}}	syncd, [2, 4, 1, 3], [4, 3, 4, 2]	4:4 , 3:3 , 3:3
7. {3, 4}	{{3, 4}}	{{2, 4}}	syncd, [2, 3, 4, 3], [4, 4, 1, 2]	2:2 , 2:2 , 3:3
8. {2, 3, 4}	{{3, 4}}	{{1, 2, 3, 4}}	syncd, [2, 4, 4, 3], [4, 3, 1, 2]	2:2 , 4:4 , 3:3

Summary

Spanning Vector: [6, 10, 12, 14]

Unicycle	Frequency	Length	Value
{1, 2, 3}	2	3	6
{3, 4}	4	2	8
{2, 4}	4	2	8
{2, 3, 4}	2	3	6
{1, 3, 4}	2	3	6
{1, 2, 3, 4}	2	4	8

Twice No. of Spanning In-Trees = 42