<｜begin▁of▁sentence｜>### Instruction:
Imagine you're working with a client who has a particular fondness for abstract art. They present you with a directional flow of influence between various hues, resembling something like an influence map of artists, but with colors guiding the aesthetic emotion of a space. This map is represented by a sequence of color transitions – where one hue leads into another, forming a directed graph.

For instance, the client gives you a sequence: Azure leads to Beige, Beige leads to Cerulean, and then Cerulean circles back to Azure, creating a cyclical pattern of influence. In the language of our influence map, this would be equivalent to `DG = nx.DiGraph([(1, 2), (2, 3), (3, 1)])`, where each number corresponds to a color.

Your task is to envisage the complete palette of influences, which includes not only direct transitions but also indirect ones. In technical terms, you're seeking the 'transitive closure' of this graph. This will show if Azure influences Cerulean, either directly or indirectly through Beige, for instance.

The challenge arises in whether to portray the self-influence of a color; this is akin to considering if a color, by virtue of a nontrivial cycle, stands on its own sufficiently enough to influence the entire space without external input. In the map, this manifests as self-loops.

So, how do we decide to display these self-references in our influence map? Should they be included or excluded based on the presence of robust cyclical patterns or a complete absence of cycles? It's a subtle but impactful choice on the eventual palette that we recommend to our client for their expressive space.
### Response:
import networkx as nx

# Create a directed graph
DG = nx.DiGraph([(1, 2), (2, 3), (3, 1)])

# Compute the transitive closure without self-loops for trivial cycles
tc_no_self_loops = nx.transitive_closure(DG, reflexive=False)
print('Transitive closure (no self-loops for trivial cycles):', tc_no_self_loops.edges())

# Compute the transitive closure with self-loops for all nodes
tc_with_self_loops = nx.transitive_closure(DG, reflexive=True)
print('Transitive closure (with self-loops for all nodes):', tc_with_self_loops.edges())

# Compute the transitive closure without any self-loops (even for nontrivial cycles)
tc_no_self_loops_at_all = nx.transitive_closure(DG, reflexive=None)
print('Transitive closure (without any self-loops):', tc_no_self_loops_at_all.edges())
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