Network theory has unveiled the underlying structure of complex systems such
as the Internet or the biological networks in the cell. It has identified
universal properties of complex networks, and the interplay between their
structure and dynamics. After almost twenty years of the field, new challenges
lie ahead. These challenges concern the multilayer structure of most of the
networks, the formulation of a network geometry and topology, and the
development of a quantum theory of networks. Making progress on these aspects
of network theory can open new venues to address interdisciplinary and physics
challenges including progress on brain dynamics, new insights into quantum
technologies, and quantum gravity.Comment: (7 pages, 4 figures
