Ok, I am startingg a social network and before I go on let me state; I haven't even seen The Social Network Movie I was looking around for base softwares and lots of people recommended a plugin for wordpress called buddypress. It is a plugin that adds new features and converts existing features to a social networking style website.
See the demo: testbp.org (you must sugn up at demo site to test it our)
Would it be a good idea to start a social network based on this (plugin for wordpress) software or should I look for a 100% social networking software?
This depends what you intend to do with the social network because you've got some ridiculous competition in that department. Social networks like Tumblr only continue to run with competition like Facebook because there is a niche for them, but if you want to make an 'everything' network like Facebook or Google+ then you may as well quit now unless you have a few million dollars to throw into it.
I dabbled in this a little while back and ended up canning it cause I had to many projects going. Buddypress is ok, but the best part is the availability of plugins. If you go this route, consider http://www.WPMUDev.org
If not, Social Engine is pretty good but spendy, or you can use Boonex Dolphin (a dating engine but good and easy to convert to any social network theme).
Buddypress is a bad idea if you are going to start a social network. Its like tweaking a Forum software to make a static site, instead of using a premade template or CMS.
And as others said, there are tons of social networks out there. So making a general one using a non-custom script is worthless.
I run the largest storm chasing/severe weather social network online. I use a free software which is like buddypress provided by www.sharetronix.com, however, it doesn't suit me so much these days so I am getting ready to convert it to www.phpfox.com which I have already purchased. Php Fox is more like twitter, FB and YouTube all in one. 🙂