Two nodes with self-loops only: equal rank (no cross-edges).

Nodes with gaps in IDs: phantom nodes in the gap are dangling.

Test image embedding with each embedder.

Test that auto modality correctly detects image.

Integer weights should be accepted and produce valid results.

Test that a missing column raises KeyError.

Test that an invalid modality raises ValueError.

Full pipeline: KNN arrays -> edges -> PageRank scores.

A long chain requires many iterations; verify it converges.

Large node IDs should work (array is sized max_id + 1).

With max_iterations=1, result should not fully converge on asymmetric graph.

Edges with vastly different weight magnitudes. In a 2-node graph each node has one outgoing edge, so after column-normalization both

If n is too small for the edge node IDs, raise ValueError.

Negative weights are not rejected (no validation), but result should still be a numpy array. This documents current behavior.

Test that the neighbors column contains dicts with 'ids' and 'distances' keys.

Test that neighbors column is not added when neighbors=None.

Test that without retries, errors are raised immediately.

Output should be float64 (from PyTorch float64 computation).

Test that results are returned in the correct order despite async execution.

Test that original DataFrame columns are preserved in the result.

Test that retries work when function fails.

Test that compute_projection returns a new DataFrame, preserving the original.

Return type must be np.ndarray, not a torch tensor.

Graph with self-loops mixed with real edges should converge.