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### Finding all digraphs up to isomorphism for a given undirected graph using Sage

Given an undirected finite connected graph (without loops). I have two questions:

1. Is there an easy way using Sage to obtain all ways to make it a directed graph (such that for each edge there is now one directed edge) up to isomorphism of graphs?

2. Is there an easy way using Sage to obtain all ways to make it a directed graph up to isomorphism of graphs and such that additionally the two opposite directed graphs get also identified?

Interesting examples might be algebras of Dynkin type such as E_8.

For $A_3$ for example in the first question there are 3 ways to make it into a directed graph. In the second question there are two ways for $A_3$.

### Finding all digraphs up to isomorphism for a given undirected graph using Sage

Given an undirected finite connected graph (without loops). I have two questions:

1. Is there an easy way using Sage to obtain all ways to make it a directed graph (such that for each edge there is now one directed edge) up to isomorphism of graphs?

2. Is there an easy way using Sage to obtain all ways to make it a directed graph up to isomorphism of graphs and such that additionally the two opposite directed graphs get also identified?

Interesting examples might be algebras graphs of Dynkin type such as E_8.

For $A_3$ for example in the first question there are 3 ways to make it into a directed graph. In the second question there are two ways for $A_3$.

### Finding all digraphs up to isomorphism for a given undirected graph using Sage

Given an undirected finite connected graph (without loops). I have two questions:

1. Is there an easy way using Sage to obtain all ways to make it a directed graph (such that for each edge there is now one directed edge) up to isomorphism of graphs?

2. Is there an easy way using Sage to obtain all ways to make it a directed graph up to isomorphism of graphs and such that additionally the two opposite directed graphs get also identified?

Interesting examples might be graphs of Dynkin type such as E_8.

For $A_3$ for example in the first question there are 3 ways to make it into a directed graph. In the second question there are two ways for $A_3$.

So the input should be a undirected finite connected graph and the output all possible orientations up to graph isomorphisms (and maybe up to taking the opposite graph as in question 2).