Proposal: update semantics for nonisomorphic trees with order 0 or 1

[rossbar]

While putting together an NX guide, I noticed a few (what I believe to be) inconsistencies in nonisomorphic_trees and number_of_nonisomorphic_trees, specifically for n = 0 and n = 1.

Currently, these functions simply raise a ValueError (with no exception message!) when n < 2. However, I think this is inconsistent with the definition of a tree, both generally and as used elsewhere in the library. For example, a graph with a single node and no edges is technically a tree:

>>> nx.is_tree(nx.empty_graph(1))
True

is_tree raises a PointlessConcept exception for the null graph (i.e. no nodes or edges), which makes sense. However, I don't think nx.number_of_nonisomorphic_trees should raise in that case (nor nx.nonisomorphic_trees, though this is subjective - see inline comment for details).

Proposed semantics

I propose to change the behavior of nx.nonisomorphic_trees and nx.number_of_nonisomorphic_trees for order=0 and order=1. I went about this in a test-driven manner, so the first commit 9de48f2 captures the proposed changes most clearly (the order < 0 case is consistent with current behavior, albeit with an added message to the ValueError)

[Peiffap]

The order==1 case is wrong I think.

Other than that: I see your nit_list and I raise you... my list of nits.

[Peiffap]

Nit, and it doesn't matter here, but since Ale just mentioned it it's fresh in my mind. We can avoid loading the whole list in memory.

Suggested change

	assert len(list(nx.nonisomorphic_trees(n))) == nx.number_of_nonisomorphic_trees(n)
	assert sum(1 for _ in nx.nonisomorphic_trees(n)) == nx.number_of_nonisomorphic_trees(n)

[rossbar]

The memory footprint is negligible here, and I personally prefer the former pattern for readability when memory/performance is not a consideration. Just my 2c though!

[dschult]

This looks good to me -- raise for negative order, yield nothing (raise StopIteration) for zero order. Use len(list(...)) instead of sum(1 for _ in ...)

Thanks for clearing up the corner cases!

[Peiffap]

All punctuation or style recs, take 'em or leave 'em. LGTM!

[Peiffap]

This avoids having to use seen, especially since we already have nit_list. Not necessarily better, your call!

Suggested change

	>>> seen = []
	>>> for G in nx.nonisomorphic_trees(n):
	... assert not any(nx.is_isomorphic(G, H) for H in seen)
	... seen.append(G)
	>>> for i, G in enumerate(nit_list):
	... assert not any(nx.is_isomorphic(G, H) for H in nit_list[i + 1:])

[dschult]

This has had many eyes and a fair amount of time -- discussion has all been in agreement and 2 approvals (and the author makes a 2nd core approval).
I'm merging it. Thanks everyone!