Robust sort_backbone: detect disconnected selections and avoid infinite loops

[DrDomenicoMarson]

Fixes #5112

Problem:

sort_backbone can hang indefinitely when the input AtomGroup is disconnected (e.g., some backbone atoms were excluded by selection). Currently, the function only checks n_fragments, which is insufficient to catch all cases of disconnected backbones.

Cause:

1. The reliance on n_fragments alone does not reliably detect disconnected selections.
2. The while loop in sort_backbone iterates until the backbone is fully traversed, but if the selection is disconnected, the loop can never complete.

Solution / Changes made:

1. Added robust validation before the traversal, checking:

   • Each atom’s connectivity degree: 1 for caps, 2 for internal atoms
   • No atom has a degree outside {1, 2}
   • Exactly two cap atoms exist
   • Added final sanity check after traversal (ensure the sorted backbone has the same length as the input)
   • All error messages now report the problematic atoms to help with debugging.

2. Replaced the “dangerous” unbounded while loop with a bounded iteration over the backbone length.

Tested with backbone selections missing internal atoms, that now raises a descriptive ValueError instead of hanging.

PR Checklist

• Issue raised/referenced?
• Tests updated/added?
• Documentation updated/added? No change needed?
• package/CHANGELOG file updated?
• Is your name in package/AUTHORS? (If it is not, add it!)

Developers Certificate of Origin

I certify that I can submit this code contribution as described in the Developer Certificate of Origin, under the MDAnalysis LICENSE.

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📚 Documentation preview 📚: https://mdanalysis--5113.org.readthedocs.build/en/5113/

[codecov]

Codecov Report

❌ Patch coverage is 80.00000% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 93.86%. Comparing base (5d48c5c) to head (b26705c).

Files with missing lines	Patch %	Lines
package/MDAnalysis/analysis/polymer.py	80.00%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #5113      +/-   ##
===========================================
- Coverage    93.86%   93.86%   -0.01%     
===========================================
  Files          179      179              
  Lines        22249    22250       +1     
  Branches      3161     3161              
===========================================
- Hits         20885    20884       -1     
- Misses         902      903       +1     
- Partials       462      463       +1     

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[tylerjereddy]

When writing new tests it might be preferable to use the built-in match=... argument of pytest.raises() to check the error message that way. It is also borderline if we should just parametrize this test with the one above it--perhaps they're different enough not to bother.

[tylerjereddy]

maybe just match=... here too