Rigid vs floppy clusters · transition at ⟨k⟩ ≈ 2.4
Network Parameters
Edges: —
Rigid bonds: —
Floppy modes: —
Max rigid cluster: —
State: —
Red bonds = rigid (pebble-covered)
Blue = floppy
Nodes coloured by cluster
The pebble game (Jacobs & Hendrickson 1997) identifies rigid vs floppy bonds in 2D networks. Each node gets 2 pebbles (2 DOF in 2D). Each bond requires 1 pebble from its neighbourhood; if found, bond is rigid. The rigidity percolation transition occurs at mean degree ⟨k⟩ = 2r = 2×2 = 4 DOF per bond → ⟨k⟩ ≈ 2.4 in 2D, distinct from connectivity percolation at ⟨k⟩ = 1.