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Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices.

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FIG. 1. (Color online) Illustration of regular square (a), regular kagome (b), generic square (c), and generic kagome lattices (d) with nearest-neighbor (NN) bonds (black, thin) and random NNN braces (red, thick)
FIG. 2. (Color online) One example of the mapping of braced regular square lattices to bipartite graphs
FIG. 5. (Color online) Probability of rigidity percolation P rigid on (a) generic square lattices and (b) generic kagome lattices as a function of N b /N M
FIG. 6. (Color online) Average number of floppy modes F  of (a) generic square and (b) generic kagome lattices as a function of N b /N M on a semilog plot
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