In order to illustrate the adaptation of traditional contin- uum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolv- ing 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 Inte- gration (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 anal., PCA) and nonlin- ear (diffusion maps, DMAPS) to determine good macroscopic variables (observables) through which one can coarse-grain the model. These re- sults suggest methods for decreasing simulation times of dynamic real- world systems such as epidemiol. network models. Addnl., the data-mining techniques could be applied to a diverse class of prob- lems to search for a succint, low-dimensional description of the system in a small number of variables.