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MaximumNeighborhoodMultiplicity on LabeledGraph ​

The most vertices that have the same set of neighbors.

On LabeledGraph

FindStat's St000723. The graph with no vertices gives 0.

Called as CombinatorialStat(x, "MaximumNeighborhoodMultiplicity"). 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 St000723

The maximal cardinality of a set of vertices with the same neighbourhood in a graph.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000723 has the rest.