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The hyperbolic brain

2020/04/05   |   academic

Structural brain networks are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Euclidean space is typically assumed as the natural geometry of the brain. However, distances in hyperbolic space offer a more accurate interpretation of the structure of connectomes across species.

Mercator

2019/12/05   |   academic

NETS2MAPS - Mercator is a new embedding tool to create maps of networks in the hyperbolic plane. Download it now from GitHub! Mercator is a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The algorithm mixes machine learning and maximum likelihood approaches to infer the coordinates of the nodes in the underlying hyperbolic disk with the best matching between the observed network topology and the geometric model. Overall, our results suggest that mixing machine learning and maximum likelihood techniques in a model-dependent framework can boost the meaningful mapping of complex networks.

Renormalizing complex networks

2019/03/20   |   academic

Maps of complex networks in hyperbolic space are not only attractive visual representations but they are full of meaning and allow us to find out information on the systems and to navigate through them. We can increase the system navigability if we take into account the information provided by the renormalization group, which allows us to unfold networks at the different structural scales that build them up, and which, in addition, turn out to be self-similar, that is, they have the same organization at different scales. These results can also be applied to make reduced versions of the original networks at smaller scales and which have the same properties. The possibility of having reduced copies has a great potential; for instance, they can serve as testbeds to assess expensive processes in original networks, such as new Internet routing protocols.





latest publications


Small worlds and clustering in spatial networks

Marián Boguñá, Dmitri Krioukov, Pedro Almagro, M. Ángeles Serrano
Phys. Rev. Research 2 023040 (2020)
theory of complex networks  |  network geometry

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Navigable maps of structural brain networks across species

Antoine Allard, M. Ángeles Serrano
PLoS Computational Biology 16 e1007584 (2020)
systems biology  |  brain


Mercator: uncovering faithful hyperbolic embeddings of complex networks

Guillermo Garcia-Perez, Antoine Allard, M. Ángeles Serrano and Marián Boguñá
New Journal of Physics 21 123033 (2019)
theory of complex networks  |  network geometry