 A graph is rigid in this sense if and only if it has a Laman subgraph that spans all of its vertices.Thus, the Laman graphs are exactly the minimally rigid graphs, and they form the bases of the two-dimensional rigidity matroids.If "n" points in the plane are given, then there are 2"n" degrees of freedom in their placement (each point has two independent coordinates), but a rigid graph has only three degrees of freedom (the position of a single one of its vertices and the rotation of the remaining graph around that vertex).