Network science is a hot and high-impact field. With critical behavior in topological random networks under scrutiny over the past decade, many questions dealing with phase transitions in graphs and networks spread far beyond pure academic interest and play a crucial role in various branches of physics (structure of membranes, formation of cosmic webs), technology (transport optimization, critical properties of electric networks), and life sciences and medicine (epidemic spread, structure of the connectome, analysis of genomic and protein networks). Investigating critical and collective effects in graphs and networks has picked up speed as a developing interdisciplinary area, with diverse applications and a variety of questions remaining to be answered. One of the most intriguing deals with the design of networks of special topology under evolution where some control parameters are changing. Many-body interactions, beyond the free-field theory, play a crucial role in network statistics. Those interactions lead to the emergence of phase transitions in complex distributed systems, and classical methods of the theory of complex networks are particularly useful in neurobiology and medicine, especially in the context of COVID-19. Throughout the workshop, we plan to focus on the statistical and dynamic properties of epidemic networks.