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Non-Euclidean Spring Embedders

2005
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IEEE Transactions on Visualization and Computer Graphics
*

The method relies on extending the

doi:10.1109/tvcg.2005.103
pmid:16270867
fatcat:nhshmnhfrngdfbcuh4ezg6b3xi
*Euclidean*notions of distance, angle, and force-interactions to smooth*non*-*Euclidean*geometries via projections to and from appropriately chosen tangent spaces. ... Generalizing the*non*-*Euclidean**spring**embedders*along the lines of [5, 7] should be possible. ... Spherical Geometry As a further example for generalizing*spring**embedders*to*non*-*Euclidean*geometry we also consider spherical geometry. ...##
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Non-Euclidean Spring Embedders

*
IEEE Symposium on Information Visualization
*

The method relies on extending the

doi:10.1109/infvis.2004.49
dblp:conf/infovis/KobourovW04
fatcat:3p7fmrvlxjhdjh4swksmyh2jgi
*Euclidean*notions of distance, angle, and force-interactions to smooth*non*-*Euclidean*geometries via projections to and from appropriately chosen tangent spaces. ... Generalizing the*non*-*Euclidean**spring**embedders*along the lines of [5, 7] should be possible. ... placement(n, G ) position[n] := τ −1 x (x ) end end Figure 4 : 4 A generic*Euclidean**spring**embedder*and its*non*-*Euclidean*counterpart. ...##
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Methodology and Techniques
[chapter]

2012
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Developments in Sedimentology
*

The method relies on extending the

doi:10.1016/b978-0-444-53813-0.00009-5
fatcat:ojtyvy2asnhm7mhuhhmf65li7q
*Euclidean*notions of distance, angle, and force-interactions to smooth*non*-*Euclidean*geometries via projections to and from appropriately chosen tangent spaces. ... Generalizing the*non*-*Euclidean**spring**embedders*along the lines of [5, 7] should be possible. ... placement(n, G ) position[n] := τ −1 x (x ) end end Figure 4 : 4 A generic*Euclidean**spring**embedder*and its*non*-*Euclidean*counterpart. ...##
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Automatic graph clustering (system demonstration)
[chapter]

1997
*
Lecture Notes in Computer Science
*

As

doi:10.1007/3-540-62495-3_63
fatcat:yysfcaeewrdh3jpnozhxpgfo2e
*spring*-*embedder*drawings tend to have related nodes close to each other, geometric proximity and statistical techniques [5] may be applied to compute clusterings from*spring*-*embedder*drawings as well ... One possible technique to visualize clusterings is to apply a*spring*-*embedder*algorithm [4] . ...##
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Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

2018
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Symposium on Experimental and Efficient Algorithms
*

Finally we explore the use of spherical drawings as initial layouts for (

doi:10.4230/lipics.sea.2018.24
dblp:conf/wea/AleardiDF18
fatcat:oonyafnkirdkjmwdr6csmzzfei
*Euclidean*)*spring**embedders*: experimental evidence shows that this greatly helps to untangle the layout and to reach better local ... While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and*spring**embedders*. ... (Spherical)*Spring**Embedders*. While*spring**embedders*are originally designed to produce 2D or 3D layouts, one can adapt them to*non**euclidean*geometries. ...##
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The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

2020
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Applied Network Science
*

This paper introduces the strain elevation tension

doi:10.1007/s41109-020-00329-4
fatcat:dzimluwdtrh2lmc3njhfmkerte
*spring*embedding (SETSe) algorithm. ... SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-*Euclidean*properties. ... It should also be noted that although SETSe is embedded in*Euclidean*space and the graph space, other*non*-*Euclidean*spaces can be used. ...##
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Spring Embedders and Force Directed Graph Drawing Algorithms
[article]

2012
*
arXiv
*
pre-print

Also known as

arXiv:1201.3011v1
fatcat:ndxz6xgx7fdkthtloaty5en2fq
*spring**embedders*, such algorithms calculate the layout of a graph using only information contained within the structure of the graph itself, rather than relying on domain-specific knowledge ... Then we obtain pseudo-code for a traditional*Euclidean**spring**embedder*and its corresponding Riemannian counterpart; see Algorithm 8. ...*Non*-*Euclidean*Approaches Much of the work on*non*-*Euclidean*graph drawing has been done in hyperbolic space which offers certain advantages over*Euclidean*space; see Munzner [52, 54] . ...##
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On graphical representations of similarity in geo-temporal frequency data

2016
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Journal of Archaeological Science
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Distance scaling (Gansner et al., 2005) , on the other hand, is the use of

doi:10.1016/j.jas.2016.05.013
fatcat:sn2ifoxjivbvrfhdakfzyumxgu
*non*-metric MDS (Kruskal, 1964) for graph layout and can be viewed as a special type of*spring*-*embedder*with*springs*of various ... We also note that common*spring*-*embedder*algorithms do not result in layouts that can be interpreted reliably. ...##
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Self-Referential Noise and the Synthesis of Three-Dimensional Space

2000
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General Relativity and Gravitation
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We argue that this is relevant to modelling the universe and show how three-dimensional space may arise from a

doi:10.1023/a:1001984518976
fatcat:bnewekbt5zb5pd3arb5q6ul4gu
*non*-geometric order-disorder model driven by self-referential noise. ... The measure V corresponds to a*spring*embedding model in which the*spring*between monad i and j has*spring*constant κ = B 2 ij , and natural length 1/|B ij |. ...*embeddability*. ...##
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The spring bounces back: Introducing the Strain Elevation Tension Spring embedding algorithm for network representation
[article]

2020
*
arXiv
*
pre-print

This paper introduces the Strain Elevation Tension

arXiv:2007.09437v1
fatcat:lesyl7zjwbhqrczl633njb5nzy
*Spring*embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks ... These algorithms are sometimes called '*spring**embedders*' [17] due to using*springs*or*spring*-like methods to place nodes and typically attempt to optimise an ideal distance between nodes, minimising ... SETSe space is a*non*-*Euclidean*metric space of n + 1 dimensions where n is the number of attributes the network has. The n + 1th dimension is the graph space, representing the graph adjacency matrix. ...##
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A Characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability

2011
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Mathematical Research Letters
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We characterize uniformly perfect, complete, doubling metric spaces, which embed bi-Lipschitzly into

doi:10.4310/mrl.2011.v18.n6.a9
fatcat:nearlydovjccpeq6q3d4qodjve
*Euclidean*space. ... We prove that if the Whitney cubes embed uniformly bi-Lipschitzly into a fixed*Euclidean*space, and if the complement of Ω also embeds, then so does the full space. Received by the editors xxx. ... Mackay when I took reading courses in Fall 2009 and in*Spring*2010. I also want to thank Jang-Mei Wu, John P. D'Angelo, and Sergiy Merenkov for their careful reading and comments. ...##
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A Characterization of Bi-Lipschitz Embeddable Metric Spaces in Terms of Local Bi-Lipschitz Embeddability
[article]

2011
*
arXiv
*
pre-print

We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into

arXiv:1105.2529v1
fatcat:coe7ltprevfevegxoze6fpzhim
*Euclidean*space. ... We prove that if the Whitney cubes embed uniformly bi-Lipschitzly into a fixed*Euclidean*space, and if the complement of Ω also embeds, then so does the full space. ... is not bi-Lipschitzly*embeddable*into any*Euclidean*space. ...##
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Drawing graphs using modular decomposition

2007
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Journal of Graph Algorithms and Applications
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In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a well-known

doi:10.7155/jgaa.00155
fatcat:dxobmywkdzbv7eqtpcszpxyz5u
*spring**embedder*algorithm. ... It turns out, that for some classes of graphs, our algorithm runs in O(n + m) time, while in general, the running time is bounded in terms of the processing time of the*spring**embedder*algorithm. ... Modified*Spring**Embedder*In this section we describe in detail a*spring**embedder*algorithm for the implementation of function Draw Prime. Recall that this function is applied on an N-node t ∈ T (G). ...##
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Drawing Graphs Using Modular Decomposition
[chapter]

2006
*
Lecture Notes in Computer Science
*

In order to achieve aesthetically pleasing results, we use grid and circular placement techniques, and utilize an appropriate modification of a well-known

doi:10.1007/11618058_31
fatcat:jtektwfdn5dl5evytclh7zgw6i
*spring**embedder*algorithm. ... It turns out, that for some classes of graphs, our algorithm runs in O(n + m) time, while in general, the running time is bounded in terms of the processing time of the*spring**embedder*algorithm. ... Modified*Spring**Embedder*In this section we describe in detail a*spring**embedder*algorithm for the implementation of function Draw Prime. Recall that this function is applied on an N-node t ∈ T (G). ...##
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eulerForce: Force-directed layout for Euler diagrams

2014
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Journal of Visual Languages and Computing
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However, current automatic methods often produce diagrams with irregular,

doi:10.1016/j.jvlc.2014.09.002
fatcat:32nnhvt7gzcudjtefpvlcswwsy
*non*-smooth curves that are not easily distinguishable. ... One of the simplest forcedirected methods is the*spring**embedder*[6] . ... Our repulsive forces are the same as those used in Eades'*spring**embedder*[6] . ...
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