A transitive relation is one where if the relation holds between A and B and also holds between B and C, it must hold between A and C. Thus, 'is taller than' is a transitive relation because if I am taller than you and you are taller than your dog Fido, then I am taller than your dog Fido. On the other hand, 'is friends with' is an intransitive relation because Nadine can be friends with Ned and Ned be friends with Noreen without it having to be the case that Nadine is friends with Noreen. Nadine might be friends with Noreen, but it doesn't follow simply from her friendship with Ned and his with Noreen that she is. Intransitive is not like antitransitive where if A stands in the given relation to B and B in that same relation to C, it follows that A can't stand in the said relation to C. Antitransitive in this way is the relation 'lives 100 miles due south of', since if you live 100 miles due south of me and I live 100 miles due south of the Doge of Draxbridge, you cannot possibly live 100 miles due south of the Doge, not that Doge anyway.
What does this have to do with Twitter? Don't be impatient; I'm getting there. Following someone on Twitter is an intransitive relation. If A follows B and B follows C, it does not follow (sic) that A follows C. A might follow C, so the relation is not antitransitive, but she doesn't necessarily follow C, so the relation is intransitive rather than transitive.
However, there is a kind of partial transitivity that operates on Twitter, on account of the practice of retweeting. If your tweets appear in my timeline, because I follow you, and Meryl Heimschmeryl's tweets appear in your timeline, because you follow her, then Meryl Heimschmeryl's tweets will also appear in my timeline when you retweet them. I call this conditional Twitter transitivity. And I have noted over my time on Twitter that other Twittizens sometimes complain of its effects. They complain when, for example, someone whom they follow retweets the tweets of someone else whom they disfavour. The complainants will then say, for example, 'Oh no, the tweets of this shmendrik [or a more insulting term yet] are being retweeted to me. Bloody hell etc.'
I find this to be both a pointless and an unjust complaint. It is pointless and unjust because what the retweeter does to you, you do willy-nilly to others unless you never, for your own part, retweet anything. You may be happy to follow Berel Heimschmerel and to retweet his stuff but he could be to some of your followers what Meryl Heimschmeryl is to you. It's a case, in this case, of (loosely) symmetrical relations: someone retweets to you the tweets of a person you would prefer not to have in your timeline; and you retweet to them, or to someone else, the tweets of a person they would prefer not to have in their timeline.
Furthermore, one has to add to this putative disbenefit of conditional Twitter transitivity an undoubted benefit of it. This is that, leaving aside the transmission of material coming from shmendriks and worse, there is the interesting stuff you see on Twitter only because it has been retweeted to you from people you don't follow by people you do follow and which you otherwise wouldn't.
