  We propose and illustrate an approach to coarse-graining the dynamics of
evolving networks (networks whose connectivity changes dynamically). The
approach is based on the equation-free framework: short bursts of detailed
network evolution simulations are coupled with lifting and restriction
operators that translate between actual network realizations and their
(appropriately chosen) coarse observables. This framework is used here to
accelerate temporal simulations (through coarse projective integration), and to
implement coarsegrained fixed point algorithms (through matrix-free
Newton-Krylov GMRES). The approach is illustrated through a simple network
evolution example, for which analytical approximations to the coarse-grained
dynamics can be independently obtained, so as to validate the computational
results. The scope and applicability of the approach, as well as the issue of
selection of good coarse observables are discussed.
