In February 6th's Fortune, there is an extract from 'The Startup of You' a new book by the founder of Linkedin. To be clear, I haven't read the book, just this extract, but two things struck me.
First, the extract says building a genuine relationship with another person depends on amongst other things: "being able to think about how you can collaborate with and help the other person rather than thinking about what you can get...start with a friendly gesture and mean it". Sounds pretty close to our guidance :-)
Second: the best networks are "wide and (selectively) deep". "The best professional network is both narrow/deep (allies with whom you collaborate regularly) and wide/shallow (weak-tie acquaintances who offer fresh information and ideas)". And, as Career Tools tells you, since you can't know early on who you'll need, just add people to your network, without thinking about their value.
The article offers an action tip which might be helpful: "Imagine you got laid off from your job today. Who are the 10 people you'd email for advice? Don't wait - invest in those relationships now".