***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 $i$. 


1. 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.
2. 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?


[***Web link to the figures***](http://postimg.org/image/wso4dgqnf/)


***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?



When does the rigidity matrix of a graph have full row rank?
The term used by Connelly and Whiteley is self-stressed, and they discuss this notion extensively in their paper "[Second-Order Rigidity and Prestress Stability for Tensegrity Frameworks](http://dx.doi.org/10.1137/S0895480192229236)."


