# Finding minimal separators between pairs of non adjacent vertices

Hello,
I am trying to find all the minimal separators between pairs of non adjacent vertices.

For now I created a basic graph following the tutorial but I am stuck.

There is a function as explained in https://igraph.org/c/doc/igraph-Iterators.html#igraph_vs_nonadj to find the non adjacent vertices of a given vertex but it seems that this option is only available in C and I would like to use Python.
What I would like to have is a list of pairs of non adjacent vertices.

Same for the minimal separators function as in https://igraph.org/c/doc/igraph-Separators.html#igraph_is_minimal_separator.

This is the code I wrote until now.

``````from igraph import *
g = Graph([(0,1), (0,2), (2,3), (3,4), (4,2), (2,5), (5,0), (6,3), (5,6)])
layout = g.layout("kk")
g.vs["label"] = g.vs.indices
plot(g, layout = layout, bbox = (300, 300), margin = 40)
``````

Could you please provide guidance on how to use these functions in Python?

Thank you very much.

Michelangelo

If your graph is relatively small, then you can achieve this with some basic Python coding. Assuming that your graph is undirected:

``````from itertools import combinations

nonadjacent_pairs = sorted(set(combinations(range(graph.vcount()), 2)) - set(graph.get_edgelist()))
``````

The minimal separators function is a method on the Graph object.

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