I've a dataset and I want to implement K-Means, Fuzzy C Means, Gaussian Mixture Model, Spectral Graph. After that, I want to see the clusters that I get from different methods. What is the proper way to do that? Or should I only stick one algorithm and try to maximize correctness of that clustering?
Have a look at the scikit learn API, they have a section dedicated to this topic.
If you want to go further, have a look at chapter 3 "Unsupervised Learning and Preprocessing" of the book Introduction to Machine Learning with Python: A Guide for Data Scientists, there is a section on clustering methods (they also mention the evaluation of clustering methods which is very insightful)