Community detection in graphs is a large topic. You can read an introduction e.g. here:
There are multiple commonly used methods for community detection. Mathematica implements several of these, but the details of the algorithms are not documented. You can look at the Method option of FindGraphCommunities and take reasonable guesses at what general type of method each of the possible settings uses (e.g. I expected "Centrality" to use the Girvan-Newman method).
To get the details on each method, I suggest you contact Wolfram Support. Personally, I found them to be helpful on most occasions (though others have sometimes reported a refusal to disclose the algorithm details...)
As you can see, you're not the first to ask about this:
As I mentioned in an answer to the second linked question above, the IGraph/M package exposes several community detection methods implemented in igraph. The igraph documentation usually has references to the original papers that introduced these methods.
