In the spirit of the past CCEGN workshops, the CCEGN-2019 continues to explore the topics at the interface between network science, statistical physics, and random graphs. The CCEGN-2019 will bring together top researchers working in these areas. The workshop aims at facilitating the transfer of ideas, insights and interdisciplinary approaches to tackle new and exciting problems in random graphs and real networks. Topics include: - Spreading phenomena and other dynamical process on networks, Griffits phases and spectral methods - Metric structure of random graphs, and spatially embedded random graphs - Random graphs with quenched disorder, microcanonical and canonical ensembles of random graphs, phase transitions, belief propagation and related questions - Statistical methods in interdisciplinary applications: social and ecological networks, genomic networks, neuroscience.