Identifier
Mp00046: Ordered trees —to graph⟶ Graphs
Mp00275: Graphs —to edge-partition of connected components⟶ Integer partitions
Images
[] => ([],1) => []
[[]] => ([(0,1)],2) => [1]
[[],[]] => ([(0,2),(1,2)],3) => [2]
[[[]]] => ([(0,2),(1,2)],3) => [2]
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => [3]
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => [3]
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => [3]
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => [3]
[[[[]]]] => ([(0,3),(1,2),(2,3)],4) => [3]
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => [4]
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [4]
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [4]
[[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [4]
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => [4]
[[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [4]
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [4]
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5]
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5]
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5]
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5]
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5]
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5]
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5]
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5]
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [5]
[[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5]
[[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [5]
[[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [5]
[[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [5]
[[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [5]
[[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [5]
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6]
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[],[],[[],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[],[[[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[]],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[],[[],[[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [6]
[[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
>>> Load all 197 entries. <<<
[[],[[[[]]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[],[[[],[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[[[]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
[[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[]],[],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [6]
[[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[]],[[[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[]],[[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[]],[[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[]],[[[],[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[]],[[[[]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]]],[],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]]],[[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[[],[]],[[[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[]]],[[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[]]],[[[]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[],[[]]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]],[]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[[[[]]]],[],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[],[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[]],[]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[],[]]],[[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[[]]]],[[]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[],[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [6]
[[[[],[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[]]],[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[[],[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[]],[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6]
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[],[[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[],[[],[[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[[],[[[[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[[]],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[]],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[[],[]],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[]]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [6]
[[[[],[[]]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[]],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [6]
[[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [6]
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[],[[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[]],[],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [6]
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [6]
[[[[[[]]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [6]
[[[[[],[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[[]],[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [6]
[[[[[[],[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [6]
[[[[[[[]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [6]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
to edge-partition of connected components
Description
Sends a graph to the partition recording the number of edges in its connected components.