  The concept of universality has shaped our understanding of many-body
physics, but is mostly limited to homogenous systems. Here, we present a study
of universality on a non-homogeneous graph, the long-range diluted graph
(LRDG). Its scaling theory is controlled by a single parameter, the spectral
dimension $d_{s}$, which plays the role of the relevant parameter on complex
geometries. The graph under consideration allows us to tune the value of the
spectral dimension continuously also to noninteger values and to find the
universal exponents as continuous functions of the dimension. By means of
extensive numerical simulations, we probe the scaling exponents of a simple
instance of $O(\mathcal{N})$ symmetric models on the LRDG showing quantitative
agreement with the theoretical prediction of universal scaling in real
dimensions.
