I have a large number of indoor cats -- that is, they have given up being ferel and either hang around the house (eating inside when they feel like coming in), or the spend the bulk of their time draped over furniture, bookcases, the bed, the TV, etc. There are often territorial disputes, but only a few of them try it on from time to time to be alpha. Since I feel comfortable with all my cats (and know just how far I can push them when it comes to shove), I watch for the following signs:
The Stare. When I see one cat get that that fixed lion-stare while focusing on another cat, I step in immediately. I either get between them, or put my hands or whatever I have in my hands (book, newspaper, pillow, towel...even a small piece of paper or other object) about 6 or 7 inches away from the cat's eyes to make it difficult for it to maintain the Stare. The cat will often bob its head from side-to-side to try to keep the Stare going, but I just follow the bobs and after a few minutes reach over and massage the cat's neck gently while telling it that it isn't nice to fight. It is the firm and loving tone of voice that helps, plus the massage, which loosens tense muscles used in maintaining the posture of aggression. If the cat is really angry, I use a more commanding tone and fix my own eyes on the cat's, which cause it to blink and look away. All the aggression starts with that Stare, and it is important to break the focus. I DO NOT try to pick up the aggressive cat. I may, in an emergency, pick up the victim by the scruff of the neck and very quickly (like playing "hot potato") deposit him/her on a nearby high spot (dresser, bed) and move off fast. This usually works just fine and everything will simmer down. When I think I can, I pet either or both cats and talk to them. They know better than to fight, but the mood just takes them over to try to kick up some trouble. It's a cat thing.
When you know your cats, you can actually break the mood when two cats are almost ready to launch at each other by putting your hands in front of both sets of eyes and commanding them to STOP IT! in a loud voice. But if you do not know them well, or trust their affection for you, don't try that.
Occasionally they get at each other when I am not nearby (it is a tiny house, so that means that I am outside or gone to town, since everywhere in the house is nearby). So some fur flies, one cat turns tail, and an hour or so later comes back to eat or drink as if nothing happened. They rarely really injure each other, and scratches -- even bloody ones -- usually don't bother them very much -- their ski is literally thicker than ours (put an antibiotic ointment on scratches to help healing -- I make my own gel from the pulp of aloe and olive oil, which works better than commercial concoctions).
When a cat does not sleep in the house but only comes in to eat or drink, the house cats sometimes treat it roughly. I will try the vanilla trick, which I did not know about. It may just work (but it means using a lot of vanilla -- I presently have 26 cats coming in for the winter).
The major thing about aggression is that it is natural to some cats, even when neutered or spayed, and so you have to be a little extra vigilant all the time. Like having two kids who are always shoving and pinching at each other. You train yourself subconsciously to watch for the danger signs. In cats, first there is the Stare, then one cat (often the endangered one) will yowl and begin to flatten its ears and hiss. Then there is a yowling contest and some posturing. If it gets to the blood-drawing stage, you need to insert a broom between them and yell. At that point the cats are beyond reason and unable to stop themselves until one triumphs. So catch it early and catch it often at the Stare stage, and the cats will begin to understand that you really will not put up with the behavior.
PS -- when bitten, let the bite bleed out -- if it doesn't bleed well, squeeze it gently to get the blood flowing. Then wash vigorously with a washcloth and soap and water. In 9 years I have had a bite get infected only once, and that was a time I was helping the vet neuter a cat on the diningroom table, and the cat objected to the anesthetic jab. We were busy, so the vet insisted that I pour some iodine (which he had in his bag) over the bite. I did so and had an infection that lingered for three weeks and required antibiotics. I will not try that advice again...