===============
Primitive rings
===============


A primitive ring is a cycle that survives the Franzblau shortest-path test.
For every pair of vertices on the cycle, a shortest path between them lies on the cycle.
``pydseams.band.ring_census`` counts those rings on ``Frame.bonds_by_index``.
For an oxygen-only frame that list is the cutoff neighbour list.

The runnable copy is ``docs/tutorials/test_rings.py``.

.. code:: python

    import pydseams as ds
    from pydseams.band import ring_census

    frame = ds.read("input/traj/exampleTraj.lammpstrj", atom_type=2)
    print(ring_census(frame, max_size=8))

On the 250 oxygens the census is 1 three-ring, 230 four-rings, 4 five-rings, and 192 six-rings.
The CLI CHILL+ graph is the mutual four-nearest list, so a census of that graph is a different number.