# scipy.cluster.hierarchy.is_isomorphic¶

scipy.cluster.hierarchy.is_isomorphic(T1, T2)[source]

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.

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


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