  We analyze the entropic equation of state for a many-particle interacting
system in a scale-free network. The analysis is performed in terms of scaling
functions which are of fundamental interest in the theory of critical phenomena
and have previously been theoretically and experimentally explored in the
context of various magnetic, fluid, and superconducting systems in two and
three dimensions. Here, we obtain general scaling functions for the entropy,
the constant-field heat capacity, and the isothermal magnetocaloric coefficient
near the critical point in scale-free networks, where the node-degree
distribution exponent $\lambda$ appears to be a global variable and plays a
crucial role, similar to the dimensionality $d$ for systems on lattices. This
extends the principle of universality to systems on scale-free networks and
allows quantification of the impact of fluctuations in the network structure on
critical behavior.
