Fix CI failure due to AZP multiple valid MST

[gegen07]

Summary

• Read the issue comment here. TLDR; the MST of scipy.sparse graphs generates some fluctuations. Then the proposed fix is presented in util.py. Working with an undirected graph give the same results over the python versions.

• MST of an unweighted graph is all trees (a path with a single component). Then it would give more than one valid MST using the scipy algorithm. Thus, I computed the distance between centroid polygons based on Queen Weight contiguity to generate a unique valid MST based on Mexico shapefile in test_azp.py.

• I changed the expected labels in the test to consider all work done in the PR.

[codecov]

Codecov Report

Merging #406 (343ef27) into main (5b7c29c) will increase coverage by 0.1%.
The diff coverage is 100.0%.

@@           Coverage Diff           @@
##            main    #406     +/-   ##
=======================================
+ Coverage   77.6%   77.7%   +0.1%     
=======================================
  Files         27      27             
  Lines       2634    2636      +2     
=======================================
+ Hits        2045    2048      +3     
+ Misses       589     588      -1     

Files	Coverage Δ
spopt/region/util.py	63.7% <100.0%> (ø)

... and 2 files with indirect coverage changes

[jGaboardi]

@gegen07 This is great work in finding the exact cause of the discrepency here. While the solution here is probably not the most efficient, it certainly does get the job done and makes CI green again (which is a huge accomplishment).

Here's a couple of points to start off the discussion:

• I computed the distance between centroid polygons based on Queen Weight contiguity to generate a unique valid MST

  • So will this distance method need to be added into AZP itself to ensure user results are reproducible?
• I am curious how the new Graph class might fit in here.

@knaaptime @martinfleis What are yalls thoughts on this?

[jGaboardi]

I'm also wondering if functions like generate_initial_sol() might be better place within azp_util.py since it's only used for AZP stuff.

[jGaboardi]

New failures due to pysal/libpysal#605, pysal/esda#271. Fix is on the way. --> pysal/esda#272

[ljwolf]

I think you can use a classic trick here:

symmetric_mst = (mst + mst.T) > 0

[jGaboardi]

@ljwolf How does this look?

[gegen07]

This is so smooth!

[jGaboardi]

@gegen07 I know, right? Always some tricks to learn that I have never seen!

[jGaboardi]

I think this is ready to go in my opinion, but we'll wait for @ljwolf' s approval to see if there are any more easy improvements.