Embedding Networks in Hyperbolic Spaces
Last update: 21 Apr 2025 21:17
First version:
An idea for generating lots of the properties commonly observed
of complex networks --- highly-skewed
degree distributions especially --- from a nice, continuous underlying
manifold.
See also:
Analysis of Network Data;
Statistics on Manifolds
Recommended:
- Reka Albert, Bhaskar DasGupta, Nasim Mobasheri, "Topological implications of negative curvature for biological and social networks", arxiv:1403.1228
- Evgeni Begelfor and Michael Werman, "The World is not Always Flat, or, Learning Curved Manifolds" [PDF]
- Andrej Cvetkovski, Mark Crovella, "Multidimensional Scaling in the Poincare Disk", arxiv:1105.5332
- R. Kleinberg, "Geographic Routing Using Hyperbolic Space",
26th IEEE Conference on Computer Communications [INFOCOM 2007], pp. 1902--1909
- Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, Marian Boguna, "Hyperbolic Geometry of Complex Networks", Physical Review E 82 (2010): 036106, arxiv:1006.5169
- Dmitri Krioukov, Fragkiskos Papadopoulos, Amin Vahdat, Marian Boguna, "Curvature and temperature of complex networks", Physical Review E 80 (2009): 035101, arxiv:0903.2584
- Fragkiskos Papadopoulos, Dmitri Krioukov, Marian Boguna, Amin Vahdat, "Greedy Forwarding in Dynamic Scale-Free Networks Embedded in Hyperbolic Metric Spaces", arxiv:0805.1266
Modesty forbids me to recommend:
- Dena Asta and CRS, "Geometric Network Comparison", UAI 2015, arxiv:1411.1350
- CRS and Dena Asta, "Consistency of Maximum Likelihood for Continuous-Space Network Models, Part I", Electronic Journal of Statisticsforthcoming (2024?), arxiv:1711.02123
To read:
- T. Aste, T. Di Matteo, S. T. Hyde, "Complex Networks on Hyperbolic Surfaces", Physica A 346 (2005): 20--26, arxiv:0408443
- Luca Gugelmann, Konstantinos Panagiotou, Ueli Peter, "Random Hyperbolic Graphs: Degree Sequence and Clustering", arxiv:1205.1470
- Kevin Verbeek and Subhash Suri, "Metric Embedding, Hyperbolic Space, and Social Networks", Proceedings of the 30th Annual Symposium on Computational Geometry [SOCG 14]
To write:
- Dena Asta and CRS, "Nonparametric Network Modeling in Hyperbolic Space"
- CRS and Dena Asta, "Consistency of Maximum Likelihood for Continuous-Space Network Models, Part II"