Mapping real networks in hidden geometry

Throughout history, maps have been pivotal in shaping political, economic, and geostrategic decisions, becoming a essential part of our daily live. They serve as reliable sources of information, offering precise and relevant data. Yet, their significance extends far beyond visual appeal. Maps serve multiple purposes: they store and present information, communicate findings, reveal locational distributions and spatial patterns, and help us conceptualize spatial processes.In our ongoing quest to comprehend complex systems across diverse domains, we have advanced the science of mapping to uncover the hidden geometry of real networks. Among our recent breakthroughs is D-Mercator, a novel embedding method rooted in geometric network models. D-Mercator empowers the creation of multidimensional maps of real networks within hyperbolic space, shedding light on their intricate connectivity. By harnessing a D-dimensional spherical similarity space and a popularity dimension, D-Mercator delineates effective hyperbolic distances between nodes, with the likelihood of connections decreasing as distance increases. This innovative approach enables us to delve deeper into the essence of real networks, capturing their intrinsic dimensionality, navigability properties, and community structure.