## The presence of angular constraints allows compositely crosslinked networks to have a finite rigidity even for small concentration of filaments.

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Figure (a) shows how the rigidity percolation threshold can be continuously lowered by increasing the probability (concentration) of angular springs for flexible (solid, blue) and stiff (dashed, red) networks. The lines correspond to the effective medium theory and the symbols to the numerical simulation. Figures (b) and (c) show the shear modulus (in logarithmic scale described by the colorbar) as a function of and for flexible networks (b) and semiflexible networks (c). The parameter values studied are (b) and (c) The black dashed lines in (b) and (c) correspond to the effective medium theory prediction of the rigidity percolation threshold. For the flexible networks, while for the semiflexible networks,