  In this paper, we consider a time-dependent discrete network model with
highly varying connectivity. The approximation by time is performed using an
implicit scheme. We propose the coarse scale approximation construction of
network models based on the Generalized Multiscale Finite Element Method. An
accurate coarse-scale approximation is generated by solving local spectral
problems in sub-networks. Convergence analysis of the proposed method is
presented for semi-discrete and discrete network models. We establish the
stability of the multiscale discrete network. Numerical results are presented
for structured and random heterogeneous networks.
