Skip to main content
`Ctrl`+`K`
scipy.cluster.hierarchy.

# is_isomorphic

scipy.cluster.hierarchy.is_isomorphic(T1, T2)

  Determine if two different cluster assignments are equivalent.

  Parameters:
    T1array_like

      An assignment of singleton cluster ids to flat cluster ids.

    T2array_like

      An assignment of singleton cluster ids to flat cluster ids.

  Returns:
    bbool

      Whether the flat cluster assignments T1 and T2 are equivalent.

  See also

  `linkage`

    for a description of what a linkage matrix is.

  `fcluster`

    for the creation of flat cluster assignments.

  Notes

  Array API support (experimental): If the input is a lazy Array (e.g. Dask or JAX), the return value will be a 0-dimensional bool Array.

  `is_isomorphic` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ⛔
  PyTorch | ✅ | ⛔
  JAX | ⚠️ see notes | ⛔
  Dask | ⚠️ see notes | n/a

  See Support for the array API standard for more information.

  Examples

      >>> from scipy.cluster.hierarchy import fcluster, is_isomorphic
      >>> from scipy.cluster.hierarchy import single, complete
      >>> from scipy.spatial.distance import pdist

  Two flat cluster assignments can be isomorphic if they represent the same cluster assignment, with different labels.

  For example, we can use the `scipy.cluster.hierarchy.single` method and flatten the output to four clusters:

      >>> X = [[0, 0], [0, 1], [1, 0],
      ...      [0, 4], [0, 3], [1, 4],
      ...      [4, 0], [3, 0], [4, 1],
      ...      [4, 4], [3, 4], [4, 3]]

      >>> Z = single(pdist(X))
      >>> T = fcluster(Z, 1, criterion='distance')
      >>> T
      array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)

  We can then do the same using the `scipy.cluster.hierarchy.complete`: method:

      >>> Z = complete(pdist(X))
      >>> T_ = fcluster(Z, 1.5, criterion='distance')
      >>> T_
      array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)

  As we can see, in both cases we obtain four clusters and all the data points are distributed in the same way - the only thing that changes are the flat cluster labels (3 => 1, 4 =>2, 2 =>3 and 4 =>1), so both cluster assignments are isomorphic:

      >>> is_isomorphic(T, T_)
      True