That is just one type of community.

What kind of community isn't centered around some form of shared values or common interests?

what about the original form of community: physical location -- the one we spent deep history evolving to be suited to navigate with wetware, instinct, intuition and body language, and from which initial social behaviour emerged :)

That clearly is not an answer the question asked.

If common interests are defined too narrowly or arbitrarily, you don't get much community.