The -dimensional
rigidity matrix
of a graph with vertex count, edge count in the variables is the matrix with rows indexed by the edges and columns
indexed by the variables in , in which the entry in row and columns is
(1)
The rigidity matrix of a framework is the matrix obtained from by replacing by for all vertices.
Connelly, R. and Guest, S. D. Frameworks, Tensegrities and Symmetry. Cambridge, England: Cambridge University Press, 2022.Grasegger,
G. "RigiComp--a Mathematica Package for Computational Rigidity of Graphs."
Dec. 19, 2022. https://zenodo.org/record/7457820#.Y7V1Ay-B30o.Grasegger,
G. "Minimal Counterexamples to Hendrickson's Conjecture on Globally Rigid Graphs."
Examples and Counterexamples3, 100106, 2023.Graver, J.;
Servatius, B.; and Servatius, H. Combinatorial
Rigidity. Providence, RI: Amer. Math. Soc., 1993.Roth, B. "Rigid
and Flexible Frameworks." Amer. Math. Monthly88, 6-21, 1981.Sitharam,
M.; St. John, A.; and Sidman, J. (Eds.). Handbook of Geometric Constraint
Systems Principles. Boca Raton, FL: CRC Press, 2018.
-dimensional
rigidity matrix 
of a graph 
with vertex count 
, edge count 
in the variables 
is the 
matrix with rows indexed by the edges and columns
indexed by the variables in 
, in which the entry in row 
and columns 
is
is the matrix 
obtained from 
by replacing 
by 
for all vertices.
