The Hidden Geometry of Complex Networks
Professor M. Ángeles Serrano (Universitat de Barcelona)
Complex networks can be successfully coupled to hidden metric spaces, in which distances between nodes determine their likelihood of interaction. This approach has offered a geometric interpretation for the complex topologies and weighted organization observed in real networks, and for their evolution and growth. Moreover, the two equivalent formulations of the family of hidden metric space network models --the Newtonian in terms of a gravity-like connection probability and the Einstenian, purely geometric in hyperbolic space-- bridge the two separate traditions of gravity models and latent space models as isomorphic counterparts. Maps of real networks embedded into a hidden metric space enable their efficient navigation without a knowledge of the complete structure, sheds light on the cross-talk of biochemical pathways in cells, and unveils the evolution of hierarchies and communities in the world trade web. A number of topics will be covered in the near future, from structural and functional geometric renormalization of complex networks to distance-based link prediction in multiplexes.
Professor M. Ángeles Serrano (Universitat de Barcelona)
Complex networks can be successfully coupled to hidden metric spaces, in which distances between nodes determine their likelihood of interaction. This approach has offered a geometric interpretation for the complex topologies and weighted organization observed in real networks, and for their evolution and growth. Moreover, the two equivalent formulations of the family of hidden metric space network models --the Newtonian in terms of a gravity-like connection probability and the Einstenian, purely geometric in hyperbolic space-- bridge the two separate traditions of gravity models and latent space models as isomorphic counterparts. Maps of real networks embedded into a hidden metric space enable their efficient navigation without a knowledge of the complete structure, sheds light on the cross-talk of biochemical pathways in cells, and unveils the evolution of hierarchies and communities in the world trade web. A number of topics will be covered in the near future, from structural and functional geometric renormalization of complex networks to distance-based link prediction in multiplexes.
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