  Disordered spring networks are a useful paradigm to examine macroscopic
mechanical properties of amorphous materials. Here, we study the elastic
behavior of under-constrained spring networks, i.e.\ networks with more degrees
of freedom than springs. While such networks are usually floppy, they can be
rigidified by applying external strain. Recently, an analytical formalism has
been developed to predict the mechanical network properties close to this
rigidity transition. Here we numerically show that these predictions apply to
many different classes of spring networks, including phantom triangular,
Delaunay, Voronoi, and honeycomb networks. The analytical predictions further
imply that the shear modulus $G$ scales linearly with isotropic stress $T$
close to the rigidity transition; however, this seems to be at odds with recent
numerical studies suggesting an exponent between $G$ and $T$ that is smaller
than one for some network classes. Using increased numerical precision and
shear stabilization, we demonstrate here that close to the transition linear
scaling, $G\sim T$, holds independent of the network class. Finally, we show
that our results are not or only weakly affected by finite-size effects,
depending on the network class.
