Force-based algorithms (graph drawing) — http://en.wikipedia.org/wiki/Force-based_algorithms_(graph_drawing)

gistfile1.txt

Pseudocode

Each node has x,y position and dx,dy velocity and mass m. There is usually a spring constant, s, and damping: 0 < damping < 1. The force toward and away from nodes is calculated according to Hooke's Law and Coulomb's law or similar as discussed above.
 set up initial node velocities to (0,0)
 set up initial node positions randomly // make sure no 2 nodes are in exactly the same position
 loop
     total_kinetic_energy := 0 // running sum of total kinetic energy over all particles
     for each node
         net-force := (0, 0) // running sum of total force on this particular node
         
         for each other node
             net-force := net-force + Coulomb_repulsion( this_node, other_node )
         next node
         
         for each spring connected to this node
             net-force := net-force + Hooke_attraction( this_node, spring )
         next spring
         
         // without damping, it moves forever
         this_node.velocity := (this_node.velocity + timestep * net-force) * damping
         this_node.position := this_node.position + timestep * this_node.velocity
         total_kinetic_energy := total_kinetic_energy + this_node.mass * (this_node.velocity)^2
     next node
 until total_kinetic_energy is less than some small number  // the simulation has stopped moving