Here's my Last.FM home link. Last.FM is a audioscrobbler-related streaming service. It uses friend network and listening stats (provided by audioscrobbler) as its outstanding feature of social software. As Anil says and it can be clearly seen in Flickr example, social networking is a "feature", not an "application" itself.
In Japan, there're two popular Social Networking services: mixi and GREE. Now I clearly come to a conclusion that mixi is a diary-oriented (or blog shared with friends) community service with social networking as a "feature".