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