Do you need to run the layout functions from JavaScript?

Create an instance of the respective layout class and call its Arrange method, or is there something more specific you need?

The only layout class that guarantees there won't be crossings if the underlying graph is planar is OrthogonalLayout.

For SpringLayout, set MinimizeLinkCrossings = true and run more iterations; that usually manages to remove the crossings.

LayeredLayout always tries to minimize crossings, but it doesn't guarantee there won't be ones. Still if your graph is planar and not very dense, it usually draws the graph without crossings.

Stoyan