How we cite our quotes:
[Edward to Bella:] "[Carlisle] was studying in Italy when he discovered the others there. They were much more civilized and educated than the wraiths of the London sewers." (16.58)
Edward tells Bella the story of Carlisle's and about the extreme isolation he had felt when he first became a vampire. Carlisle was surprised to find others who were sophisticated like him. However, he remained isolated because of his "vegetarian" diet. Until he created his own family, Carlisle was pretty much alone.
[Esme to Bella:] "That's why I'm so happy that he's found you, dear. […] He's been the odd man out far too long; it's hurt me to see him alone." (17.279)
Esme feels like a mom to Edward and is thrilled he now has someone to love. Even though Edward has a great family, he was somewhat isolated since all of the other Cullens were paired off.
[Alice to Bella:] "It's been almost a century that Edward's been alone. Now he's found you. You can't see the changes that we see, we who have been with him for so long. Do you think any of us want to look into his eyes for the next hundred years if he loses you?" (20.51)
Alice echoes Esme's earlier sentiment that Edward has led a lonely life. Now, the Cullens are willing to fight James in order to ensure Edward's happiness.