- FindStat

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Identifier

St000265: Graphs ⟶ ℤ

Values

([],1) => 0

([],2) => 0

([(0,1)],2) => 1

([],3) => 0

([(1,2)],3) => 1

([(0,2),(1,2)],3) => 4

([(0,1),(0,2),(1,2)],3) => 3

([],4) => 0

([(2,3)],4) => 1

([(1,3),(2,3)],4) => 4

([(0,3),(1,3),(2,3)],4) => 9

([(0,3),(1,2)],4) => 2

([(0,3),(1,2),(2,3)],4) => 10

([(1,2),(1,3),(2,3)],4) => 3

([(0,3),(1,2),(1,3),(2,3)],4) => 8

([(0,2),(0,3),(1,2),(1,3)],4) => 8

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 7

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 6

([],5) => 0

([(3,4)],5) => 1

([(2,4),(3,4)],5) => 4

([(1,4),(2,4),(3,4)],5) => 9

([(0,4),(1,4),(2,4),(3,4)],5) => 16

([(1,4),(2,3)],5) => 2

([(1,4),(2,3),(3,4)],5) => 10

([(0,1),(2,4),(3,4)],5) => 5

([(2,3),(2,4),(3,4)],5) => 3

([(0,4),(1,4),(2,3),(3,4)],5) => 18

([(1,4),(2,3),(2,4),(3,4)],5) => 8

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 15

([(1,3),(1,4),(2,3),(2,4)],5) => 8

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 16

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 7

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 16

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 14

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 14

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 13

([(0,4),(1,3),(2,3),(2,4)],5) => 20

([(0,1),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 17

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 14

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 15

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 14

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 13

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 15

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 6

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 13

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 12

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 13

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 12

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 11

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 10

([],6) => 0

([(4,5)],6) => 1

([(3,5),(4,5)],6) => 4

([(2,5),(3,5),(4,5)],6) => 9

([(1,5),(2,5),(3,5),(4,5)],6) => 16

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 25

([(2,5),(3,4)],6) => 2

([(2,5),(3,4),(4,5)],6) => 10

([(1,2),(3,5),(4,5)],6) => 5

([(3,4),(3,5),(4,5)],6) => 3

([(1,5),(2,5),(3,4),(4,5)],6) => 18

([(0,1),(2,5),(3,5),(4,5)],6) => 10

([(2,5),(3,4),(3,5),(4,5)],6) => 8

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 28

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 15

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 24

([(2,4),(2,5),(3,4),(3,5)],6) => 8

([(0,5),(1,5),(2,4),(3,4)],6) => 8

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 16

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 32

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 7

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 16

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 29

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 26

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 14

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 26

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 23

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 14

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 28

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 24

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 13

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 24

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 22

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 22

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 21

([(0,5),(1,4),(2,3)],6) => 3

([(1,5),(2,4),(3,4),(3,5)],6) => 20

([(0,1),(2,5),(3,4),(4,5)],6) => 11

([(1,2),(3,4),(3,5),(4,5)],6) => 4

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 31

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 17

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 9

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 27

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 14

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 23

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 15

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 27

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 14

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 26

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Description

The Wiener index of a graph.
This is the sum of the distances of all pairs of vertices.

References

[1] wikipedia:Wiener index
[2] Knor, M., Škrekovski, R., Tepeh, A. Mathematical aspects of Wiener index arXiv:1510.00800
[3] Georgakopoulos, A., Wagner, S. Hitting Times, Cover Cost, and the Wiener Index of a Tree arXiv:1302.3212

Code

def statistic(g):
    if g.order() < 2:
        return 0
    if g.is_connected():
        return g.copy(immutable=True).wiener_index()
    else:
        return sum( statistic(h.copy(immutable=True)) for h in g.connected_components_subgraphs() )

Created

Jul 27, 2015 at 17:29 by Martin Rubey

Updated

Aug 10, 2016 at 14:48 by Martin Rubey