No team is your rival (moreso than others) until the collective sentiment of your fans, players and the community that claims you has that "rival feeling"... and vice versa. We are not (yet) rivals with ULM, in anything. It just has not happened. Unfortunately, I think we are heading down that path. We are losing touch with LaTech and Tulane, and some other programs that a rivalry was in process, in football in particular.
I think our SBC foes in football have not established a single rivalry for us. There is a slight start here and there, but there is no team that has us feeling a "rivalry" in football that stands out from the rest.
I kind of liken a rival to someone you hate so much, or absolutely love to beat so much, that you are thinking about them (as fans) many games ahead of playing them. Over the years of being in the SBC, I have yet to look at the schedule in search of a specific school's name, on a certain date, and my lip curl and low growl come out, as a I see their name on the schedule. Nope... that has not happened for us yet. And definitely not with ULM.