When we consider multilayer networks, we typically think about multiplex or interconnected complex networks. There is, however, another category of multilayerty embodied in the form of a multilayer network shell that distinguishes the coexisting scales in the structure of a complex network and how they are interrelated. The multiscale unfolding is generated by applying a geometric renormalization protocol acting on the geometric representation of a complex network in hyperbolic space, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure. We found that multiscale multilayer shells of real networks, including connectomes of the human brain, show multiscale self-similarity, which is also found in the evolution of some growing real networks, suggesting that evolutionary processes can be modeled by reversing renormalization. Multiscale network shells afford us immediate practical applications, including high-fidelity scaled down and scaled up replicas of real networks and a multiscale navigation protocol in hyperbolic space, which betters performance on single layers.
M. Ángeles Serrano is an ICREA Research Professor at the Department of Condensed Matter Physics of the University of Barcelona (UB). She obtained her Ph.D. in Physics at UB with a thesis about gravitational wave detection, and a master in mathematics for finance from the Centre de Recerca Matemàtica CRM. After four years in the private sector as IT consultant and mutual fund manager, she returned to academia in 2004 to work in the field of complex networks. She completed her postdoctoral research at Indiana University (USA), the École Polytechnique Fédérale de Lausanne (Switzerland) and IFISC Institute (Spain). She came back to Barcelona in 2009, when she was awarded a Ramón y Cajal Fellowship at UB. M. Ángeles obtained the Outstanding Referee Award of the American Physical Society. She is a founding member of Complexitat, the Catalan network for the study of complex systems, and a promoter member of UBICS, the Universitat de Barcelona Institute of Complex Systems.