In the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Euclidean space. In a rigidity matroid for a graph with n vertices in d-dimensional space, a set of edges that defines a subgraph with k degrees of freedom has matroid rankdn − k. A set of edges is independent if and only if, for every edge in the set, removing the edge would increase the number of degrees of freedom of the remaining subgraph.[1][2][3]
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