Ask Your Question

# Random orientation of a graph

Is there a command to randomly orient a graph? (no additional edges) not the to_directed command

edit retag close merge delete

## Comments

Congratulations for asking this question.

Adding such a method to Sage is now tracked at Sage trac ticket #25303: Random orientation of a graph.

( 2018-05-07 11:39:52 -0500 )edit

## 1 answer

Sort by » oldest newest most voted

Picking each edge and applying a random orientation is a one-liner.

For example, starting from the Petersen graph:

sage: G = graphs.PetersenGraph(); G
Petersen graph: Graph on 10 vertices


we can apply a random orientation to each edge:

sage: DiGraph([(a, b, c) if randint(0, 1) else (b, a, c) for a, b, c in G.edge_iterator()])
Digraph on 10 vertices


To make reuse easier, we write a function to orient an edge at random as follows:

def orient_edge_at_random((a, b, c)):
r"""
Return this edge with a random orientation

An edge consists of a start vertex, end vertex, and a label.
At random, we switch the start vertex and the end vertex.

EXAMPLE::

sage: orient_edge_at_random((0, 1, None)) # random
(0, 1, None)
sage: orient_edge_at_random((0, 1, None)) # random
(1, 0, None)
"""
if randint(0, 1):
return(a, b, c)
return(b, a, c)


and a function to orient all edges of an unoriented graph at random as follows:

def random_orientation_digraph(G):
r"""
Return a directed graph built from this undirected graph

The edges of the directed graph will be the edges of the undirected
graph, each of them being assigned an orientation at random.

EXAMPLE::

sage: G = graphs.PetersenGraph(); G
Petersen graph: Graph on 10 vertices
sage: edges = G.edge_iterator(labels=False)
sage: random_orientation_digraph(G)
Digraph on 10 vertices
"""
return(DiGraph([orient_edge_at_random(e) for e in G.edge_iterator()]))

more

## Comments

Note: a better implementation based on this proof of concept is proposed at

( 2018-05-07 11:41:52 -0500 )edit

## Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

## Stats

Asked: 2018-05-06 19:36:46 -0500

Seen: 90 times

Last updated: May 07 '18