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I'm looking to animate a graph layout using edges as springs and nodes as weights (a node with more links will have a bigger weight).

I'm not capable of wrapping my head around the usage of mathematical and physics relations in my application.

As far as I've read, Runge Kutta 4 (preferably) or Verlet will be a good choice, but I have problems with understanding how they really work, and what physics equations I should apply.

If I can't understand them, I can't use them. I'm looking for a book or a tutorial which describes the things that I need.

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can you elaborate on the shape of your graph (perhaps a sketch). If the change in Y is steady, you will most likely be fine with simple Euler integration. It is when the change in Y is fluid and you need accuracy that you consider alternatives. –  Steve H Mar 10 '11 at 4:04
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up vote 4 down vote accepted

Here is an awesome introduction to the Runge Kutta 4 integration:

http://gafferongames.com/game-physics/integration-basics/

It starts with a brief introduction to the Euler integration basics (and why you shouldn't use it).

Moreover, there are more tutorials on this page about game-physics: How to fix your timestep, physics in 3D, spring physics, and networked physics

Hope it helps!

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