Use this if you are using igraph from R
| is_separator {igraph} | R Documentation | 
Check whether a given set of vertices is a vertex separator.
is_separator(graph, candidate)
graph | 
 The input graph. It may be directed, but edge directions are ignored.  | 
candidate | 
 A numeric vector giving the vertex ids of the candidate separator.  | 
is_separator decides whether the supplied vertex set is a vertex
separator. A vertex set is a vertex separator if its removal results a
disconnected graph.
In the special case of a fully connected graph with n vertices, each
set of n-1 vertices is considered to be a vertex separator.
A logical scalar, whether the supplied vertex set is a (minimal) vertex separator or not.
is_min_separator, min_separators
lists all vertex separator of minimum size.