  With the advent of the big data era, generative models of complex networks
are becoming elusive from direct computational simulation. We present an exact,
linear-algebraic reduction scheme of generative models of networks. By
exploiting the bilinear structure of the matrix representation of the
generative model, we separate its null eigenspace, and reduce the exact
description of the generative model to a smaller vector space. After reduction,
we group generative models in universality classes according to their rank and
metric signature, and work out, in a computationally affordable way, their
relevant properties (e.g., spectrum). The reduction also provides the
environment for a simplified computation of their properties. The proposed
scheme works for any generative model admitting a matrix representation, and
will be very useful in the study of dynamical processes on networks, as well as
in the understanding of generative models to come, according to the provided
classification.
