  Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring
in topics ranging from biology and physics, to social networks and technology.
A fundamental and long-time goal in the study of synchronisation has been to
find low-order descriptions of complex oscillator networks and their collective
dynamics. However, for the Kuramoto model - the most widely used model of
coupled oscillators - this goal has remained surprisingly challenging, in
particular for finite-size networks. Here, we propose a model reduction
framework that effectively captures synchronisation behaviour in complex
network topologies. This framework generalises a collective coordinates
approach for all-to-all networks [Gottwald (2015) Chaos 25, 053111] by
incorporating the graph Laplacian matrix in the collective coordinates. We
first derive low dimensional evolution equations for both clustered and
non-clustered oscillator networks. We then demonstrate in numerical simulations
for Erdos-Renyi (ER) networks that the collective coordinates capture the
synchronisation behaviour in both finite-size networks as well as in the
thermodynamic limit, even in the presence of interacting clusters.
