  In order to illustrate the adaptation of traditional continuum numerical
techniques to the study of complex network systems, we use the equation-free
framework to analyze a dynamically evolving multigraph. This approach is based
on coupling short intervals of direct dynamic network simulation with
appropriately-defined lifting and restriction operators, mapping the detailed
network description to suitable macroscopic (coarse-grained) variables and
back. This enables the acceleration of direct simulations through Coarse
Projective Integration (CPI), as well as the identification of coarse
stationary states via a Newton-GMRES method. We also demonstrate the use of
data-mining, both linear (principal component analysis, PCA) and nonlinear
(diffusion maps, DMAPS) to determine good macroscopic variables (observables)
through which one can coarse-grain the model. These results suggest methods for
decreasing simulation times of dynamic real-world systems such as
epidemiological network models. Additionally, the data-mining techniques could
be applied to a diverse class of problems to search for a succint,
low-dimensional description of the system in a small number of variables.
