My office has just six people besides myself.
Is it appropriate to invite only the four I’m "friendly" with to a Sunday barbecue, and not the two with whom I maintain an "all business" relationship, or should I just suck it up and invite everyone?
Just don’t diss the uninvited. When inviting a select few co-workers, do it discreetly and away from the office (try calling them in the evening) to make it clear this a "nonoffice" event. Also, be careful not to rant and rave the next day in front of the uninvited about what a great time you all had. Finally, try varying your routine: Socializing with pals is fine, but consider holding get-togethers every now and then where everyone in the office is invited.
Source: Post, Peter. "Etiquette at Work." Boston Globe 10 Oct. 2004.