Editing Force-directed graph drawing (section)

==Methods==
Once the forces on the nodes and edges of a graph have been defined, the behavior of the entire graph under these sources may then be simulated as if it were a physical system. In such a simulation, the forces are applied to the nodes, pulling them closer together or pushing them further apart. This is repeated iteratively until the system comes to a [[mechanical equilibrium]] state; i.e., their relative positions do not change anymore from one iteration to the next. The positions of the nodes in this equilibrium are used to generate a drawing of the graph.

For forces defined from springs whose ideal length is proportional to the graph-theoretic distance, [[stress majorization]] gives a very well-behaved (i.e., monotonically [[limit of a sequence|convergent]])<ref name="dl88">{{citation
  | last=de Leeuw | first=Jan
  | title=Convergence of the majorization method for multidimensional scaling
  | year=1988
  | journal=Journal of Classification
  | publisher=Springer
  | volume=5 | issue=2 | pages=163&ndash;180
  | doi=10.1007/BF01897162| s2cid=122413124
 }}.</ref> and mathematically elegant way to [[optimization (mathematics)|minimize]] these differences and, hence, find a good layout for the graph.

It is also possible to employ mechanisms that search more directly for energy minima, either instead of or in conjunction with physical simulation. Such mechanisms, which are examples of general [[global optimization]] methods, include [[simulated annealing]] and [[genetic algorithm]]s.