Social networking, both online and offline, is all about meeting people and creating contacts that can enhance your personal and professional life. Each direct connection you make gives you indirect access to even more people. Facebook focuses on that personal side of social networking.
When you and your new partner connect on Facebook, you'll be able to see each other's friends, too. Facebook might even encourage you to make connections with each other's friends with its "People You May Know" feature. Facebook is a great way to meet people and grow your social network because of features like this.
In a new relationship, be cautious how you approach this network growth. Don't start making Facebook friend requests to all your partner's friends. This could come across as stalking, similar to frequently writing on someone's wall. You could also be overstepping a boundary of trust, diving in to your partner's friends list before your partner can comfortably make introductions.
If you still want to connect to someone without an introduction, carefully choose only one or two friends to befriend each week. Take time to introduce yourself in your request and say why you'd like to be connected. Remember that your partner's friends might ignore you or, worse, complain about you to your partner. To prevent these risks in a new relationship, you can also ask your partner to make the introduction so you don't seem like a stranger or stalker.