technically he is because carlisle transformed him in 1918 at his mother elizabeth's request while she was dying from the spanish influenza.carlisle took edward under his wing and cared for him as if he was his own son and soon after transformed his wife esme then rosalie and emmett.even though alice and jasper are part of the cullen's they are not infact family cause they weren't transformed द्वारा any of the other cullens it was others than turned them.emmett,edward,esme,rosalie and carlisle are family cause carlisle turned edward their for edward has carlisle in him same goes for esme,then emmett is family cause edward tuened him and he turned rosalie.alice and jasper are family cause they treat them like family but they do not have any traces of the others in them.