How to study the effect of eps in sklearn.cluster.DBSCAN? I posted this question on stackoverflow.com and have not received any answer. In case I get an answer from one of them, I will inform on the other.

I have a dataset and is requested by my professor to study the effect of eps in sklearn.cluster import DBSCAN? Could you please suggest some ways to measure its effect? I generated eps = np.arange(start = .1, stop = 1, step = .1), but I don't know what should I compare.
import numpy as np 
import pandas as pd
import matplotlib.pyplot as plt 
from sklearn.cluster import DBSCAN
%config InlineBackend.figure_format = 'svg' # Change the image format to svg for better quality
don = pd.read_csv('https://raw.githubusercontent.com/leanhdung1994/Deep-Learning/main/donclassif.txt.gz', sep=';')

kmeans = DBSCAN(eps = .2)
y_kmeans = kmeans.fit_predict(don)

plt.figure(figsize = 1.5 * np.array(plt.rcParams['figure.figsize'])) # This is to have bigger plot
plt.scatter(don['V1'], don['V2'], c = y_kmeans, cmap = 'viridis')

eps = np.arange(start = .1, stop = 1, step = .1)
The meaning of $\epsilon$ is that of the neighbourhood size. The neighbourhood of a point $p$, denoted by $N_{\epsilon}(p)$, is defined as the $N_{\epsilon}(p) = \{q \in D | dist(p,q) \leq \epsilon \}$. Here $D$ is a database of $n$ objects (points) and $q$ a query point.
So what you Professor probably wants you to do is to evaluate goodness of clustering algorithm (DBSCAN) based on its input Parameters Epsilon. This goodness of fit you can measure for example with Silhouette score