  Collective variables (CVs) are low-dimensional projections of
high-dimensional system states. They are used to gain insights into complex
emergent dynamical behaviors of processes on networks. The relation between CVs
and network measures is not well understood and its derivation typically
requires detailed knowledge of both the dynamical system and the network
topology. In this work, we present a data-driven method for algorithmically
learning and understanding CVs for binary-state spreading processes on networks
of arbitrary topology. We demonstrate our method using four example networks:
the stochastic block model, a ring-shaped graph, a random regular graph, and a
scale-free network generated by the Albert-Barab\'asi model. Our results
deliver evidence for the existence of low-dimensional CVs even in cases that
are not yet understood theoretically.
