Interdisciplinary and physics challenges of Network Theory

TL;DR

This paper reviews the progress and future challenges in network theory, emphasizing multilayer structures, network geometry, and quantum aspects, with implications for interdisciplinary fields like brain dynamics and quantum gravity.

Contribution

It highlights the emerging challenges in network theory related to multilayer networks, geometry, and quantum aspects, proposing directions for future research.

Findings

Identification of universal properties of complex networks

Discussion of multilayer network structures and their challenges

Proposal of a quantum theory of networks

Abstract

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.