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Try this code:

from sage.graphs.connectivity import vertex_connectivity
G=Graph({1:[2,3,4,5],2:[1,3,4,5],3:[1,2,4,5],4:[1,2,3],5:[1,2,3]})
vertex_connectivity(G,value_only=False)

The result, running in a SageCell Server is

(3, [1, 2, 3])

Which says the vertex connectivity is 3 and the vertices 1,2,3 are such a set.

The documentation for vertex_connectivity() is here.