We are extremely pleased to present this special issue of Network Science which contains a collection of extended papers from the Seventh International Conference on Complex Networks & their Applications (COMPLEX NETWORKS 2018). Initiated in 2011, the conference series has grown to become one of the major international events in network science. Every year, it brings together researchers from a wide variety of scientific backgrounds ranging from finance and economics, medicine and neuroscience, biology and earth sciences, sociology and political science, computer science, physics, and many others in order to review the current state of the field and formulate new directions. The great diversity of the participants allows for cross-fertilization between fundamental issues and innovative applications. COMPLEX NETWORKS 2018 was hosted at the Department of Computer Science and Technology of the University of Cambridge (UK)-a true place of innovation-from December 11 to December 13, 2018. It attracted 421 submissions originating from more than 50 countries around the world. After a rigorous reviewing process, the conference program committee selected 123 papers to be published in the conference proceedings (Aiello et al., 2018a,b). The conference program also included keynote presentations from Vittoria Colizza (INSERM,