Structural rigidity

Graphs are drawn as rods connected by rotating hinges. The cycle graph C4 drawn as a square can be tilted over by the blue force into a parallelogram, so it is a flexible graph. K3, drawn as a triangle, cannot be altered by any force that is applied to it, so it is a rigid graph.

In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.