In the Wiki:
A complete graph with n vertices, denoted $K_n$, has no vertex cuts at all.
Also, the node connectivity of a complete graph ($n$ nodes) is $n-1$
I review the definition of "vertex cut" or "cut" in wiki:
a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition.
I really have no idea why a complete graph has no vertex cut by the definition? (I can still do the following: