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Geometrical congruence and efficient greedy navigability of complex networks [article]

Carlo Vittorio Cannistraci, Alessandro Muscoloni
2020 arXiv   pre-print
This assumption of geometrical congruence is considered the reason for nearly maximally efficient greedy navigation of hyperbolic networks.  ...  We discover that, contrary to current belief, hyperbolic networks do not demonstrate in general geometrical congruence and efficient navigability which, in networks generated with nPSO model, seem to emerge  ...  Computing (ZIH) of the TU Dresden.  ... 
arXiv:2005.13255v1 fatcat:mvg2flln6jhfrkbgbmqjwibb4i

Navigable maps of structural brain networks across species

Antoine Allard, M. Ángeles Serrano, Saad Jbabdi
2020 PLoS Computational Biology  
As a navigation strategy, we use greedy routing where nearest neighbors, in terms of geometric distance, are visited.  ...  In contrast, we find that hyperbolic space, the effective geometry of complex networks, provides almost perfectly navigable maps of connectomes for all species, meaning that hyperbolic distances are exceptionally  ...  Navigable maps of structural brain networks across species  ... 
doi:10.1371/journal.pcbi.1007584 pmid:32012151 fatcat:7hxw2utp6zhw3cslu2rxmp5cwa

Navigable maps of structural brain networks across species [article]

Antoine Allard, M. Ángeles Serrano
2018 arXiv   pre-print
Here, we investigate the flow of information in connectomes of several species using greedy routing as a distributed navigation protocol.  ...  While these networks provide global connectivity and sustain the broad spectrum of the functions of the brain, the underlying routing strategies for communication between the different areas and their  ...  To do so, we consider connectomes from various species and quantify the aforementioned congruency using the efficiency of greedy routing (GR) as a distributed navigation protocol [23, 24] .  ... 
arXiv:1801.06079v1 fatcat:y6yunpniqjcqrfjoactrb23uxe

Navigability of temporal networks in hyperbolic space [article]

Elisenda Ortiz, Michele Starnini, M.Ángeles Serrano
2017 arXiv   pre-print
These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.  ...  Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies.  ...  Effects of network dynamics on navigability The success ratio p s is a key parameter in determining the navigability of complex networks.  ... 
arXiv:1709.02623v1 fatcat:yzlwkhsukrc5xij4pbwssa4tw4

Multiscale unfolding of real networks by geometric renormalization

Guillermo García-Pérez, Marián Boguñá, M. Ángeles Serrano
2018 Nature Physics  
replicas of large networks and a multiscale navigation protocol in hyperbolic space which boosts the success of single-layer versions.  ...  Here, we define a geometric renormalization group for complex networks and use the technique to investigate networks as viewed at different scales.  ...  The last property suggests a new and efficient multiscale community detection algorithm for complex networks 35-37 .  ... 
doi:10.1038/s41567-018-0072-5 fatcat:52eqb44nnvfkvohdi4jzh5pewa

Navigability of temporal networks in hyperbolic space

Elisenda Ortiz, Michele Starnini, M. Ángeles Serrano
2017 Scientific Reports  
These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.  ...  Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies.  ...  McDonnell Foundation Scholar Award in Complex Systems, the Ministerio de Economía y Competitividad of Spain projects no. FIS2013-47282-C2-1-P and no.  ... 
doi:10.1038/s41598-017-15041-0 pmid:29118421 pmcid:PMC5678097 fatcat:kg6askytcbgxpeglvdcpl2xt54

Model-free hidden geometry of complex networks [article]

Yi-Jiao Zhang, Kai-Cheng Yang, Filippo Radicchi
2020 arXiv   pre-print
Proximity can be preserved in relatively low-dimensional embedding spaces and the hidden geometry displays optimal performance in guiding greedy navigation regardless of the specific network topology.  ...  The findings deepen our understanding of the model-free hidden geometry of complex networks.  ...  Cannistraci for critical comments on an early version of the manuscript. Y.-J.Z. acknowledges support from China Scholarships Council (No.201906180029). Y.  ... 
arXiv:2011.08103v1 fatcat:xoijcswsxrak3jmoru5h4orecy

Geometric renormalization unravels self-similarity of the multiscale human connectome [article]

Muhua Zheng, Antoine Allard, Patric Hagmann, Yasser Alemán-Gómez, M. Ángeles Serrano
2020 arXiv   pre-print
Strikingly, a geometric network model, where distances are not Euclidean, predicts the multiscale properties of connectomes, including self-similarity.  ...  The model relies on the application of a geometric renormalization protocol which decreases the resolution by coarse-graining and averaging over short similarity distances.  ...  Indeed, a geometric model purely based on Euclidean distances would produce geometric random networks lacking key features of real complex networks such as the small-world property.  ... 
arXiv:1904.11793v3 fatcat:bdekvo2nyvcvdif72ionudbtc4

Hyperbolic geometry of complex networks

Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, Marián Boguñá
2010 Physical Review E  
We develop a geometric framework to study the structure and function of complex networks.  ...  We then establish a mapping between our geometric framework and statistical mechanics of complex networks.  ...  Aranovich, and others for useful discussions and suggestions. This work was supported by NSF CNS-0964236, CNS-0722070, CNS-0434996, DHS N66001-08-C-2029, FIS2007-66485-C02-02, and by Cisco Systems.  ... 
doi:10.1103/physreve.82.036106 pmid:21230138 fatcat:tqof52jv5fbprb3l5rdyf3dpaq

Systematic comparison of graph embedding methods in practical tasks [article]

Yi-Jiao Zhang, Kai-Cheng Yang, Filippo Radicchi
2021 arXiv   pre-print
Network embedding techniques aim at representing structural properties of graphs in geometric space.  ...  Three common downstream tasks -- mapping accuracy, greedy routing, and link prediction -- are considered to evaluate the quality of the various embedding methods.  ...  Greedy routing Network embeddings may be used in greedy routing protocols devised for efficient network navigation [5, 29] .  ... 
arXiv:2106.10198v1 fatcat:o2qbqww325cadkqo5jewa2oqwm

Network Mapping by Replaying Hyperbolic Growth

Fragkiskos Papadopoulos, Constantinos Psomas, Dmitri Krioukov
2015 IEEE/ACM Transactions on Networking  
that a vast majority of greedy geometric routing paths are successful and low-stretch.  ...  Recent years have shown a promising progress in understanding geometric underpinnings behind the structure, function, and dynamics of many complex networks in nature and society.  ...  Kitsak, and M. Á. Serrano for many useful discussions, and B. Huffaker for help with the AS geographic data.  ... 
doi:10.1109/tnet.2013.2294052 fatcat:beo7p2areveahj5gt4lhdlyjlu

Network Geometry [article]

Marian Boguna, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Angeles Serrano
2020 arXiv   pre-print
and challenges in this novel frontier in the study of complexity.  ...  and other forms of fundamental symmetries in networks.  ...  From a practical point of view, applications include scaled-down network replicas and a multiscale navigation protocol that takes advantage of the increased navigation efficiency at higher scales.  ... 
arXiv:2001.03241v2 fatcat:n3kqsgmpxffr5klzoihs525mrm

Image Analysis and Computer Vision: 1996

Azriel Rosenfeld
1997 Computer Vision and Image Understanding  
Weinshall, Complexity of indexing: Efficient and learnable large database indexing, IUW, 1193-1198. 626. S. Ravela, R. Manmatha, and E.M.  ...  Werman and D. Weinshall, Complexity of indexing: Efficient and learnable large database indexing, ECCV A, 660-670. 631. R. Zabih, J. Miller, and K.  ... 
doi:10.1006/cviu.1997.0602 fatcat:h4bc2zwjbjhvvjei6bl4h4pfvy

Image Analysis and Computer Vision: 1993

A Rosenfeld
1994 Computer Vision and Image Understanding  
Weinshall, Complexity of indexing: Efficient and learnable large database indexing, IUW, 1193-1198. 626. S. Ravela, R. Manmatha, and E.M.  ...  Werman and D. Weinshall, Complexity of indexing: Efficient and learnable large database indexing, ECCV A, 660-670. 631. R. Zabih, J. Miller, and K.  ... 
doi:10.1006/cviu.1994.1030 fatcat:xwof2hfiuzfwvkfnamnahk4fvi

Image analysis and computer vision: 1991

Azriel Rosenfeld
1992 CVGIP: Image Understanding  
Weinshall, Complexity of indexing: Efficient and learnable large database indexing, IUW, 1193-1198. 626. S. Ravela, R. Manmatha, and E.M.  ...  Werman and D. Weinshall, Complexity of indexing: Efficient and learnable large database indexing, ECCV A, 660-670. 631. R. Zabih, J. Miller, and K.  ... 
doi:10.1016/1049-9660(92)90032-x fatcat:hzeumdeaa5bh7jxo7vtfvexj4i
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