Martin Roulleaux Dugage provides a very interesting definition of a community versus a network or a group. A community is a network that has decided to auto-organize by adopting 6 attributes:
You are whether in or out the community
Why do we decide to stick together in the first place ? What meaning does it have ?
Community members are committed to achieve something. In that respect, for instance, active Wikipedians form a community, since they edit articles and create new ones on a regular basis.
Community is no jungle. Social interactions are governed by a set of rules, or an etiquette.
Community members share words. It can be a jargon. At any rate, it helps them communicate and create a feeling of belonging.