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

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.88%. Comparing base (5d48c5c) to head (800cbdf).
⚠️ Report is 30 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #5113      +/-   ##
===========================================
+ Coverage    93.86%   93.88%   +0.02%     
===========================================
  Files          179      180       +1     
  Lines        22249    22421     +172     
  Branches      3161     3185      +24     
===========================================
+ Hits         20885    21051     +166     
  Misses         902      902              
- Partials       462      468       +6     

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[orbeckst]

Thank you for your fix @DrDomenicoMarson ! Please address @tylerjereddy 's comments and my minor ones.

[orbeckst]

Thanks for addressing the other comments. Todo:

• check formatting (black)
• improve test coverage of patch

[orbeckst]

Not covered by tests – could you please add a test for it?

[DrDomenicoMarson]

I wrote this as a final sanity check, but when I tested the code, I realized that I can’t reach this part of the code without having the analysis fail earlier (which is what it should do, considering the situation). So, I decided to remove this “untestable and useless” part.

[orbeckst]

LGTM, thank you!

Will get into release 2.10.0.