Lost Circles (link to their website) is an extension for Google Chrome that maps your Facebook friends in a network.
Link to the Google Chrome store
My sales pitch
The software is specifically aimed at Facebook. It's not as extensive as you describe, in fact it only looks at your Facebook friends and looks which of those people are also friends with each other. Based on that it outputs a graph and shows the communities it found (probably based on some community detection algorithm, but I'm not sure).
While the software isn't as extensive as you want, it does provide an interesting insight in your own Facebook network. For example, it might show different communities for your school friends, your work colleagues and your sport-related friends (of course there would be more communities if you went to different schools, for example a high school community and a college community). Even more interesting is seeing which friends connect those communities (by also having friends in both communities)
You should consider this software because it's free (it does list a price in the Google Chrome store, but you can just click add to Chrome without paying, I think), easy to install and may provide an interesting insight. It's in no way complete in the sense that it does all you ask for, but it may well be the case that there is no one piece of software out there that does all these things (you might need different pieces of software and combine the results yourself).
As listed on their website, you might have to set your Facebook language to English for the extension to work.
Possible privacy concern
It does require giving this extension access to read data on the web pages you visit. You only need to visit Facebook and are able to delete the extension afterwards. I'm not sure if they (the makers of the extension) collect any information, I cannot vouch for them, so use it at your own risk.