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SameNeighborhoodPairCount on LabeledGraph ​

The pairs of vertices that have the same set of neighbors.

On LabeledGraph

FindStat's St001347. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "SameNeighborhoodPairCount"). The head's page has its examples.

Live

Distribution

Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St001347

The number of pairs of vertices of a graph having the same neighbourhood.

ObjectValue
([],1)0
([],2)1
([],3)3
([],4)6
([],5)10
([],6)15
([],7)21
([(0,1)],2)0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001347 has the rest.