Network Geometry

Jan 9, 2020
22 pages
Published in:
  • Nature Rev.Phys. 3 (2021) 2, 114-135
  • Published: Jan 29, 2021
e-Print:

Citations per year

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Abstract: (Springer)
The fractal geometry of networks enables casting the self-similar symmetries underlying the organization of complex systems under the three pillars of scaling, universality and renormalization.Latent metric spaces with hyperbolic geometry provide a natural explanation for the architecture of real complex networks, including small-worldness, degree heterogeneity, clustering, community structure, symmetries and navigability.Multiscale unfolding of complex networks is possible by means of a geometric renormalization technique that uncovers self-similarity at different scales.Network dynamical processes induce kinematic distances that characterize an effective geometry of a system’s function, which cannot be obtained by purely topological latent geometry.Network geometry enhances our understanding of complex systems across their multiple scales of organization and of collective phenomena emerging from their information exchange.The fractal geometry of networks enables casting the self-similar symmetries underlying the organization of complex systems under the three pillars of scaling, universality and renormalization.Latent metric spaces with hyperbolic geometry provide a natural explanation for the architecture of real complex networks, including small-worldness, degree heterogeneity, clustering, community structure, symmetries and navigability.Multiscale unfolding of complex networks is possible by means of a geometric renormalization technique that uncovers self-similarity at different scales.Network dynamical processes induce kinematic distances that characterize an effective geometry of a system’s function, which cannot be obtained by purely topological latent geometry.Network geometry enhances our understanding of complex systems across their multiple scales of organization and of collective phenomena emerging from their information exchange.