HyperWienerIndex on LabeledGraph
The sum over the pairs of vertices of their distance plus its square.
FindStat's St000467, of a connected graph; a pair with no path adds nothing. The graph with no vertices gives 0.
Called as CombinatorialStat(x, "HyperWienerIndex"). The head's page has its examples.
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Distribution
Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000467
The hyper-Wiener index of a connected graph.
| Object | Value |
|---|---|
([],1) | 0 |
([(0,1)],2) | 2 |
([(0,2),(1,2)],3) | 10 |
([(0,1),(0,2),(1,2)],3) | 6 |
([(0,3),(1,2),(2,3)],4) | 30 |
([(0,3),(1,3),(2,3)],4) | 24 |
([(0,2),(0,3),(1,2),(1,3)],4) | 20 |
([(0,3),(1,2),(1,3),(2,3)],4) | 20 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000467 has the rest.