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Complex systems are a class of systems composed of multiple elements interacting in a nonsimple way such that collective behaviors emerge. These systems can be of various natures: biological (e.g., ecosystems, microbiomes, brains), technological (e.g., the Internet, power grids), or social (e.g., contact/social networks). Their emergent behaviors are equally diverse: the stability of ecosystems under external perturbations, the flocking behavior of birds, the cognitive functions of the brain, and the susceptibility of a population to sustain an epidemic of an infectious disease.
Critically, these systems are fundamentally more than the sum of their parts, meaning that their collective dynamics are not encoded in the individual elements, but rather are the results of the complex structure of the interactions between these elements. One of the main challenges to uncover the intricate relationship between the structure and the dynamics in complex systems is therefore rooted in the complexity of the structure of the interactions itself. Mathematically, these structures are represented by complex networks (or graphs) whose topology lies somewhere between order and randomness, thereby making the design of accurate mathematical models notoriously difficult.
While geometry shapes the topology of the real complex networks embedded in physical space, it has been shown that abstract latent geometries provide a powerful modeling strategy for the real complex networks that are not embedded in a physical space. Despite many advances in recent years, the emerging field of network geometry has a rich and promising untapped potential to explore and to exploit.
This Collection aims to assemble algorithms, datasets, models, and frameworks to explore this synergy between geometry, graph theory, and complexity in general. We welcome original articles, perspective papers, and comments from all fields that contribute to a conversation across disciplines to rethink the way we model the web of interactions at the core of complex systems.