Say I am offering a sharing service where people can exchange ideas and information through a simple interface. Users can start a group conversation and add their friends to interact with. Is the word clique too pejorative to describe such a group of people?
Being a mathematician, I particularly find the word clique a very good choice, but my colleagues are afraid it might evoke restrictiveness and exclusion based on the typical "high school cliques".
Your colleagues are correct, the word has an English language meaning...
Clique: a small close-knit group of people who do not readily allow others to join them.
This suggest an unwelcoming group, or self selected group of people who aren't interested in what others have to contribute because perhaps they think they are better than the others.
When applied to people, the term tends to suggest that the people in question are unwelcoming toward others. The term is also useful in other contexts, however, such as graphing or networking theory, where it has no such connotation. If in an electronic network a group of machines said to form a clique, that would mean that every machine in the group is aware of and can communicate with every other, but no machine in the group is connected to any machine outside the group. The fact that the machines in the clique do not communicate with those outside would not be taken as any form of value judgment about whether or not such behavior is desirable or undesirable, or whether machines are "welcoming". Indeed, in the automated network scenario it is not uncommon for cliques to be quite welcoming, such that when a machine outside the clique establishes a connection to one member, all other members will automatically establish connections to it.
With regard to electronic networking systems that are used for interpersonal communication, the social and technical aspects of the word get merged; from a technical standpoint users' accounts might form cliques, but that doesn't mean that the humans associated with those accounts do so. It may be a good idea to avoid using the term "clique" in situations where the things being networked are strongly associated with individual people, but the term might be reasonable if the things are more strongly associated with non-human objects (e.g. describing toy robots as forming "cliques", even though they have human owners, would not be taken to imply any snobbishness on the part of those owners, even if describing social networking accounts in such fashion might).
Your colleagues are correct: although the dictionary definition may appear neutral, usage of the word in idiomatic English almost invariably has a pejorative/negative connotation, e.g. as per Hot Licks' comment.
