Corpus ID: 19074014

Hyperbolic grids and discrete random graphs

  title={Hyperbolic grids and discrete random graphs},
  author={Eryk Kopczy'nski and Dorota Celi'nska},
We present an efficient algorithm for computing distances in hyperbolic grids. We apply this algorithm to work efficiently with a discrete variant of the hyperbolic random graph model. This model is gaining popularity in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. We present experimental results conducted on real world networks. 
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This paper shows and experimentally analyze an efficient algorithm for generating tessellations and describes the tree structure, and explains how to use such a tree structure to generate a periodic tessellingation. Expand


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A new maximum likelihood estimation algorithm that embeds scale-free graphs in the hyperbolic space and achieves quasi-linear runtime, which makes it the first algorithm that can embed networks with hundreds of thousands of nodes in less than one hour. Expand
Generating Random Hyperbolic Graphs in Subquadratic Time
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Hyperbolic Geometry of Complex Networks
It is shown that targeted transport processes without global topology knowledge are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure. Expand
Small Universal Cellular Automata in Hyperbolic Spaces: A Collection of Jewels
Why hyperbolic geometry?.- Cellular automata and the railway model.- Inthepentagrid.- In the heptagrid.- In the tilings.- In the dodecagrid.- Strongly universal hyperbolic cellular automata.- TheExpand
Exploring Large Graphs in 3D Hyperbolic Space
  • T. Munzner
  • Computer Science
  • IEEE Computer Graphics and Applications
  • 1998
A software system that explicitly attempts to handle much larger graphs than previous systems and support dynamic exploration rather than final presentation is described and the applicability of this system to goals beyond simple exploration is discussed. Expand
Graph minors. III. Planar tree-width
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Non-Euclidean Spring Embedders
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