I don’t think you could say Alligators are ‘social’ animals. They’re cannibals at times.
If you watch them enough you do discover their habits. One is definitely a need to be close, at times, to other gators.

Above, two adult American Alligators swimming together.
ACE Basin, South Carolina.
Can’t say I have ever gotten a shot with a couple before – double trouble for any prey in the area.
I found a group feeding by an open dike once. I managed to catch 64 in one frame. Of course I was using an 18mm wide angle lens. But they were all close trying to grab fish as they came through the dike. Funny, but right in the middle was a Snowy Egret.