* Intuitive description*: In the 2D plane, there are $m$ bars connected by $n$ joints. The length of each bar is fixed. These joints and bars can be viewed as a graph (see the figures below). Denote $s_i$ as the static stress of bar $i$.

- For some graphs (see figure 1), it is clear all $s_i$ must be zero. Otherwise, the stress applied on each joint is non-zero and the graph cannot be balanced in the plane.
- For other graphs (see figure 2), some $s_i$ can be non-zero and the graph can be well balanced in the plane.

**My question**: does the later kind of graphs have a name? Any theoretical discussions on them in the literature?

* Mathematical description*: I am studying graph rigidity. Denote $$R=\mathrm{blkdiag}(e_1^T,\cdots,e_m^T)(H\otimes I_2)$$ as the rigidity matrix of a graph, where $e_i\in\mathbb{R}^2$ denotes the edge of the graph, $H\in\mathbb{R}^{m\times n}$ is the incidence matrix, and $I_2$ is the 2x2 identity matrix. The left null space of $R$ actually is the space of all non-zero stresses. So mathematically my question can be rephrased as: when is the rigidity matrix of full row rank?