made some nice tasting ones yesterday. usually I use 1 egg per pound of beef but didn't use egg yesterday as had guests that couldn't have eggs. they held together in the pan but fell apart when eating. I used 1kg ground beef 2 onions very finely chopped in a food proccessor salt pepper herbs 2 table spoons flour
Putting the onions in the food processor would have released a lot of water, I wouldn't have done that, just chopped with a knife on a board would be fine. And like cat says, you work the meat like play-doh, and they should be fine without egg.
You have to massage the meat.... squish it about, knead it, mix & stir it really well.... or mix the burgers in your food processor using the dough hook. This makes the sticky proteins in the meat come to the surface and that holds the meat together.