It depends on how you define "DB" in this context. Ex-Facebooker so I this may have changed but I doubt it. It's fairly fundamental.
At the lowest level, data is stored in MySQL so yes, that's open source. Almost nothing user-facing will talk to MySQL directly because you're bypassing all the privacy, scaling, auditing, security, etc. Some legacy systems are on different MySQL instances but we're talking internal systems, not public-facing.
The in-memory graph database on top of that, which I think you're actually referring to, is called TAO [1]. AFAIK, no, it isn't open source.
All of this is very much designed for the type of data Facebook stores and how it's used (eg "12,345 people liked this" is an easy query but listing all the things you liked can be really expensive beyond the most recent likes).
At the lowest level, data is stored in MySQL so yes, that's open source. Almost nothing user-facing will talk to MySQL directly because you're bypassing all the privacy, scaling, auditing, security, etc. Some legacy systems are on different MySQL instances but we're talking internal systems, not public-facing.
The in-memory graph database on top of that, which I think you're actually referring to, is called TAO [1]. AFAIK, no, it isn't open source.
All of this is very much designed for the type of data Facebook stores and how it's used (eg "12,345 people liked this" is an easy query but listing all the things you liked can be really expensive beyond the most recent likes).
[1]: https://engineering.fb.com/2013/06/25/core-infra/tao-the-pow...