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Hyperbolicity measures democracy in real-world networks

Michele Borassi, Alessandro Chessa, Guido Caldarelli
2015 Physical Review E  
We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation.  ...  In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks.  ...  DISCUSSION In the literature, several works have analyzed the hyperbolicity of a complex network.  ... 
doi:10.1103/physreve.92.032812 pmid:26465533 fatcat:66qthvbbjbcyxbkyejvvcrdjgm

Emergent Hyperbolic Network Geometry

Ginestra Bianconi, Christoph Rahmede
2017 Scientific Reports  
The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree  ...  Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network  ...  so far are related to the embeddings of complex networks in hyperbolic spaces [27] [28] [29] [30] 32 .  ... 
doi:10.1038/srep41974 pmid:28167818 pmcid:PMC5294422 fatcat:isyqoensvrcatgtq742ha2af7m

On Computing the Hyperbolicity of Real-World Graphs [chapter]

Michele Borassi, David Coudert, Pierluigi Crescenzi, Andrea Marino
2015 Lecture Notes in Computer Science  
, the analysis of graph algorithms, and the classification of complex networks.  ...  In this paper, we provide a new and more efficient algorithm: although its worst-case complexity is O(n 4 ), in practice it is much faster, allowing, for the first time, the computation of the hyperbolicity  ...  In the field of the analysis of complex networks, the hyperbolicity and its connection with the size and the diameter of a network has been used in [2] in order to classify networks into three different  ... 
doi:10.1007/978-3-662-48350-3_19 fatcat:ycnnz47uevgdth56acejw77gui

On Computing the Gromov Hyperbolicity

Nathann Cohen, David Coudert, Aurélien Lancin
2015 ACM Journal of Experimental Algorithmics  
The Gromov hyperbolicity is an important parameter for analyzing complex networks which expresses how the metric structure of a network looks like a tree.  ...  Its running time depends on the distribution of distances and on the actual value of the hyperbolicity.  ...  In [29] a geometric framework for studying the structure of complex networks has been proposed, which highlights the underlying hyperbolic geometry of complex networks and shows that topologies of hyperbolic  ... 
doi:10.1145/2780652 fatcat:iedavf2uhbb3fg2a2jqokbq35m

Functional Geometry of Human Connectome and Robustness of Gender Differences [article]

Bosiljka Tadic, Miroslav Andjelkovic, Roderick Melnik
2019 arXiv   pre-print
However, the latent structure on higher-order connections remains unexplored, where many brain regions acting in synergy perform complex functions.  ...  Here we analyse this hidden structure using the simplicial complexes parametrisation where the shared faces of simplexes encode higher-order relationships between groups of nodes and emerging hyperbolic  ...  MA received financial support from the Ministry of Education, Science and Technological Development of the Republic of Serbia, under the project OI 174014.  ... 
arXiv:1904.03399v1 fatcat:4v572yx2hzb45ahagfiqzf6h4u

Non-hyperbolicity in random regular graphs and their traffic characteristics

Gabriel Tucci
2013 Open Mathematics  
We also show that these graphs are not asymptotically δ-hyperbolic for any non-negative δ almost surely as n → ∞.  ...  AbstractIn this paper we prove that random d-regular graphs with d ≥ 3 have traffic congestion of the order O(n logd−13 n) where n is the number of nodes and geodesic routing is used.  ...  We would like to thank Itai Benjamini for some helpful comments and for pointing out the reference [3] .  ... 
doi:10.2478/s11533-013-0268-y fatcat:g637csoxhjbl3fhxzmujwy5zcu

Hyperbolic Trees in Complex Networks

Zalan Heszberger, Andras Gulyas, Andras Biro, Andras Majdan, Laszlo Balazs, Jozsef Biro
2020 2020 International Conference on Computational Science and Computational Intelligence (CSCI)  
, US flight network) embedded in the hyperbolic plane.  ...  We show that these hyperbolic trees have scale-free degree distributions and are present to a large extent both in synthetic hyperbolic complex networks and real ones (Internet autonomous system topology  ...  The rule significantly differs from the ones used for hyperbolic complex network generation [7] , and no other structural properties of the network are considered in the hyperbolic tree generation.  ... 
doi:10.1109/csci51800.2020.00254 fatcat:4pndb3z4gjdsnnffmh6l5kriqi

Topological estimation of the latent geometry of a complex network [article]

Bukyoung Jhun
2021 arXiv   pre-print
Inspired by the fact that long-range links in a network have disproportionately high loads, we develop a set of methods that can analyze the latent geometry of a complex network: the modified persistent  ...  The latent geometry of a complex network is a central topic of research in network science, which has an expansive range of practical applications such as efficient navigation, missing link prediction,  ...  Acknowledgments This research was supported by the NRF, Grant No. NRF-2014R1A3A2069005.  ... 
arXiv:2008.10204v3 fatcat:yadpdmpg5jhtxdqlr4sdwqwqiy

On the Hyperbolicity of Large-Scale Networks [article]

W. Sean Kennedy, Onuttom Narayan, Iraj Saniee
2013 arXiv   pre-print
, and helps classify in a parsimonious way what is otherwise a bewildering and complex array of features and characteristics specific to each natural and man-made network.  ...  In smooth geometry, hyperbolicity captures the notion of negative curvature; within the more abstract context of metric spaces, it can be generalized as d-hyperbolicity.  ...  The work of Kennedy was additionally supported by a postdoctoral grant from the Canadian NSERC.  ... 
arXiv:1307.0031v1 fatcat:xk5ejb66mjcd3gngpvjhnt367i

Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

Bosiljka Tadić, Miroslav Andjelković, Milovan Šuvakov
2018 Frontiers in Physics  
We find that the corresponding networks are δ-hyperbolic with δ max = 1 and the graph diameter D = 3 in each brain.  ...  Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function.  ...  The authors acknowledge the support for research visits from the Department of Theoretical Physics, Jožef Stefan Institute.  ... 
doi:10.3389/fphy.2018.00007 fatcat:i23fmefvq5fzvorbnmrdfplv7a

Complex Networks in the Framework of Nonassociative Geometry [article]

Alexander I. Nesterov, Pablo Héctor Mata Villafuert
2018 arXiv   pre-print
We use this approach to study the Internet as a complex network embedded in a hyperbolic space.  ...  In the scope of nonassociative geometry we present a new effective model that extends the statistical treatment of complex networks, accounting for the effect of nonlocal curvature.  ...  In what follows we explore in detail complex networks embedded in a hyperbolic space. Hyperbolic complex networks.  ... 
arXiv:1812.10865v1 fatcat:gni4a67tyrdqthun257jctki6y

Functional Geometry of Human Connectomes

Bosiljka Tadić, Miroslav Andjelković, Roderick Melnik
2019 Scientific Reports  
However, the latent structure on higher-order interactions remains unexplored, where many brain regions act in synergy to perform complex functions.  ...  These results shed new light on the functional architecture of the brain, suggesting that insightful differences among connectomes are hidden in their higher-order connectivity.  ...  MA received financial support from the Ministry of Education, Science and Technological Development of the Republic of Serbia, under the project OI 174014.  ... 
doi:10.1038/s41598-019-48568-5 pmid:31427676 pmcid:PMC6700117 fatcat:h3yruvud55fwtkz5cbe2aaycq4

Topological percolation on hyperbolic simplicial complexes

Ginestra Bianconi, Robert M. Ziff
2018 Physical review. E  
While most of the known results on percolation in hyperbolic manifolds are in d=2, here we uncover the rich critical behavior of d=3 hyperbolic manifolds, and show that triangle percolation displays a  ...  Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions.  ...  The PI is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.  ... 
doi:10.1103/physreve.98.052308 fatcat:a7hh63hguneadpiadsdruqmylm

AS path inference: From complex network perspective

Narisu Tao, Xu Chen, Xiaoming Fu
2015 2015 IFIP Networking Conference (IFIP Networking)  
In this paper, we bring a new angle to the AS path inference problem by exploiting the metrical tree-likeness or low hyperbolicity of the Internet, part of the complex network properties of the Internet  ...  With intensive evaluations on AS paths from real-world BGP Routing Information Bases, we show that the proposed new algorithms can achieve superior performance, in particular, when AS paths are long paths  ...  ACKNOWLEDGEMENT The authors would like to thank Sergey Gorinsky and anonymous reviews for their valuable comments. Thanks to the German Academic Exchange Service (DAAD) for its generous support.  ... 
doi:10.1109/ifipnetworking.2015.7145303 dblp:conf/networking/TaoCF15 fatcat:si7bwpksjregpmoyv3oi6sjehq

Random Regular Graphs are not Asymptotically Gromov Hyperbolic [article]

Gabriel H. Tucci
2012 arXiv   pre-print
We also show that these graphs are not asymptotically δ--hyperbolic for any non--negative δ almost surely as n→∞.  ...  In this paper we prove that random d--regular graphs with d≥ 3 have traffic congestion of the order O(n_d-1^3(n)) where n is the number of nodes and geodesic routing is used.  ...  It was observed in many complex networks, man-made or natural, that the typical distance between the nodes is surprisingly small.  ... 
arXiv:1203.5069v1 fatcat:3g7rjorpzbg2zmlgipwzblykz4
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