Could be one of many types of recommendation algorithms, maybe collaborative filtering?
This is just a shortest path algorithm on the social graph. Assuming there is no weight to the connections, it will simply use breadth-first.
Simply a re-arrangement of the data set using the same algorithm as People you may follow.
Check out the book Programming Collective Intelligence for a good introduction to the type of algorithms that are used for People you may follow and Similar to you, it has great python code available too.
In term of machine learning/data mining, we called these kind of problems as the classification problem. The easiest approach is to use past data for future prediction, i.e. statistical oriented:
http://en.wikipedia.org/wiki/Statistical_classification, in which you can start by using the Naive Bayes classifier (commonly used in spam detection)
I would suggest you to read this book (Although written for Python): Programming Collective Intelligence (http://www.amazon.com/Programming-Collective-Intelligence-Building-Applications/dp/0596529325), they have a good example.
This book should guide you through the steps of choosing a recommendation algorithm: http://www.amazon.com/Programming-Collective-Intelligence-Building-Applications/dp/0596529325.
It even contains the necessary code examples, although they are written in python.
Yup there are lots of algorithms. Things such as k-nearest neighbor: http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm.
Here is a pretty good book on the subject that covers making these sorts of systems along with others: http://www.amazon.com/gp/product/0596529325?ie=UTF8&tag=ianburriscom-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0596529325.
Depending on exactly what you mean by "gotten to grips with the basics", I'd suggest reading through Dive Into Python and typing/executing all the chapter code, then get something like Programming Collective Intelligence and working through it - you'll learn python quite well, not to mention some quite excellent algorithms that'll come in handy to a web developer.
Two books that cover recommender systems:
Basically two ways of approaching the problem, user or item based. Netflix appears to use the former, while Amazon the latter. Typically user based requires more time and/or processing power to generate recommendations because you tend to have more users than items to consider.
Good practical books on these kind of algorithms are:
Programming Collective Intelligence is a nice, approachable introduction to this field.
Solr 1.4 Enterprise Search Server
Programming Collective Intelligence
Building Search Applications: Lucene, LingPipe, and Gate
I think I've listened to every podcast on software engineering radio a few times . The older ones are especially nice because they usually pick a specific topic and cover the high points. I liked that I could listen to it while I was driving, or otherwise not in front of a computer.
I've also got Introduction to Algorithms, which I use as a reference, sometimes. I switched over to The Algorithm Design Manual  after I saw it referenced in an older Steve Yegge post . I read through the intro and it seemed like a book that would be more appropriate from an autodidactic standpoint. I really have no idea if that's going to pan out, since I'm not that far into it, but we'll see, for sure. Doesn't kill me to have an extra algorithms book laying about, though, and I've always got intro to algorithms for cross reference. I've found that I really need to have as many sources available as possible when I'm learning alone. Usually I don't get something until the fifth person describes it from the tenth different angle.
That's most of what I can think of off hand. I really enjoyed The Joy of Clojure , though haven't checked out the newer version. Programming Collective Intelligence  is a fun book, and is what made me want to go back down the maths route to get more into machine learning.
And of course habitually reading hacker news for an hour or three every night :)
So that's my totally inexpert list of random stuff that I enjoy