If you run a stellar-core instance, it is possible to query the quorum set for any validator via an http request on port 11626:
Here is the endpoint your would use:
And here is a description from the docs on the Stellar website:
returns information about the quorum for node NODE_ID (this node by
default). NODE_ID is either a full key (GABCD...), an alias ($name) or
an abbreviated ID (@GABCD). If compact is set, only returns a summary
If you were interested in mapping out the entirety of the network, it is possible to run a stellar-core instance, and after a while you'd have access to a local SQL database of all the peers you've seen. Currently this schema does not include validator public key, but with a few tweaks that may be possible.