Incorrect structure on random points for data with small variations. Lack of shuffling?

umap.__version__ == 0.4.6

In the following example, UMAP is applied to random data with tiny variations around a fixed value. Arbitrary labels are assigned to the data in order ('a' for the first 150 samples, 'b' to the next 150, etc.).

When applying UMAP, a structure appears (points with the same label are grouped), as shown in the image below, but it should not (random data).
This issue can potentially lead to incorrect interpretations.

It could be due to a kind of greedy behavior in the construction of the neighborhood graph.
Randomly shuffling the data before construction of the neighborhood graph solves the problem, but might not be an ideal fix.

import numpy as np
from umap import UMAP
import umap.plot

n_obs = 600
n_vars = 16
np.random.seed(42)

fixed_value = np.random.random(n_vars)
X = 10 * fixed_value + 1e-9 * np.random.random((n_obs, n_vars))
labels = np.array(['a'] * (n_obs // 4)
                  + ['b'] * (n_obs // 4)
                  + ['c'] * (n_obs // 4)
                  + ['d'] * (n_obs // 4))

reducer = UMAP(
    metric="cosine",
    min_dist=0.0,
    n_neighbors=10,
    random_state=0,
)
reducer.fit(X)
p = umap.plot.points(reducer, labels=labels, theme="fire")
umap.plot.show(p)

Start by running the provided Python reproduction with UMAP 0.4.6 and inspect the neighborhood graph construction reached by reducer.fit(X). Compare the result with and without shuffling the near-constant data; done means the embedding no longer reflects the input label order for random data.