One of the beauties of fried rice is that it will gratefully embrace just about any old leftovers you throw at it (hunks of stilton excepted) but whatever you put in, egg should be mandatory. Not only does it add protein, but a delicious richness too. When you add it, however, is up for debate.
Ching-He Huang scrambles the eggs first, then removes them from the pan while she cooks the rice, before combining the two. Allegra McEvedy "half scrambles" them in the hot wok for 20 seconds before adding the rice. Rose Prince stir-fries the rice first, then pushes it back and scrambles the egg in the centre of the pan before mixing the two together, while Ken Hom adds the beaten egg to the rice and stirs it all together so the egg is absorbed by the rice.