  The stochastic block model (SBM) is extensively used to model networks in
which users belong to certain communities. In recent years, the study of
information-theoretic compression of such networks has gained attention, with
works primarily focusing on lossless compression. In this work, we address the
lossy compression of SBM graphs by characterizing the rate-distortion function
under a Hamming distortion constraint. Specifically, we derive the conditional
rate-distortion function of the SBM with community membership as side
information. We approach this problem as the classical Wyner-Ziv lossy problem
by minimising mutual information of the graph and its reconstruction
conditioned on community labels. Lastly, we also derive the rate-distortion
function of the Erd\H{o}s-R\'enyi (ER) random graph model.
