Analyze social networks

g = ExampleData[{"NetworkGraph", "ZacharyKarateClub"}]

Graph[<34>, <78>]

VertexCount[g]

34

EdgeCount[g]

78

With[{d = DegreeCentrality[g]}, Pick[VertexList[g], d, Max[d]]]

{34}

Part[VertexList[g], Reverse[Ordering[BetweennessCentrality[g]]][[ ;; 2]]]

{1, 34}

Pick[VertexList[g], DegreeCentrality[g], 0 | 1]

{12}