Editing Force-directed graph drawing (section)

==Advantages==
The following are among the most important advantages of force-directed algorithms:
; Good-quality results: At least for graphs of medium size (up to 50–500 vertices), the results obtained have usually very good quality based on the following criteria: uniform edge length, uniform vertex distribution and showing symmetry. This last criterion is among the most important ones and is hard to achieve with any other type of algorithm.
; Flexibility: Force-directed algorithms can be easily adapted and extended to fulfill additional aesthetic criteria. This makes them the most versatile class of graph drawing algorithms. Examples of existing extensions include the ones for directed graphs, 3D graph drawing,<ref>{{citation|last=Vose|first=Aaron|title=3D Phylogenetic Tree Viewer|url=http://aaronvose.net/phytree3d/|access-date=3 June 2012}}</ref> cluster graph drawing, constrained graph drawing, and dynamic graph drawing.
; Intuitive: Since they are based on physical analogies of common objects, like springs, the behavior of the algorithms is relatively easy to predict and understand. This is not the case with other types of [[Graph drawing|graph-drawing]] algorithms.
; Simplicity: Typical force-directed algorithms are simple and can be implemented in a few lines of code. Other classes of graph-drawing algorithms, like the ones for orthogonal layouts, are usually much more involved.
; Interactivity: Another advantage of this class of algorithm is the interactive aspect. By drawing the intermediate stages of the graph, the user can follow how the graph evolves, seeing it unfold from a tangled mess into a good-looking configuration. In some interactive graph drawing tools, the user can pull one or more nodes out of their equilibrium state and watch them migrate back into position. This makes them a preferred choice for dynamic and [[online algorithm|online]] graph-drawing systems.
; Strong theoretical foundations: While simple ''ad-hoc'' force-directed algorithms often appear in the literature and in practice (because they are relatively easy to understand), more reasoned approaches are starting to gain traction. Statisticians have been solving similar problems in [[multidimensional scaling]] (MDS) since the 1930s, and physicists also have a long history of working with related [[n-body]] problems - so extremely mature approaches exist. As an example, the [[stress majorization]] approach to metric MDS can be applied to graph drawing as described above. This has been proven to [[Monotone convergence theorem|converge monotonically]].<ref name="dl88"/> Monotonic convergence, the property that the algorithm will at each iteration decrease the stress or cost of the layout, is important because it guarantees that the layout will eventually reach a local minimum and stop. Damping schedules cause the algorithm to stop, but cannot guarantee that a true local minimum is reached.