scholarly journals Clustering and the Hyperbolic Geometry of Complex Networks

2014 ◽  
pp. 1-12 ◽  
Author(s):  
Elisabetta Candellero ◽  
Nikolaos Fountoulakis
Keyword(s):  
Complex Networks ◽  
Hyperbolic Geometry

scholarly journals Clustering and the Hyperbolic Geometry of Complex Networks

2015 ◽  
Vol 12 (1-2) ◽  
pp. 2-53 ◽  
Author(s):  
Elisabetta Candellero ◽  
Nikolaos Fountoulakis
Keyword(s):  
Complex Networks ◽  
Hyperbolic Geometry

scholarly journals Hyperbolic geometry of complex networks

2010 ◽  
Vol 82 (3) ◽  
Author(s):  
Dmitri Krioukov ◽  
Fragkiskos Papadopoulos ◽  
Maksim Kitsak ◽  
Amin Vahdat ◽  
Marián Boguñá
Keyword(s):  
Complex Networks ◽  
Hyperbolic Geometry

Hyperbolic Geometry from a Local Viewpoint

2007 ◽  
Author(s):  
Linda Keen ◽  
Nikola Lakic
Keyword(s):  
Hyperbolic Geometry

Complex Networks

2009 ◽  
Author(s):  
Reuven Cohen ◽  
Shlomo Havlin
Keyword(s):  
Complex Networks

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

Complex Networks from Simple Rules

2013 ◽  
Vol 22 (2) ◽  
pp. 151-174 ◽  
Author(s):  
Richard Southwell ◽  
Jianwei Huang ◽  
Chris Cannings ◽  
◽  
Keyword(s):  
Complex Networks ◽  
Simple Rules
Sign in / Sign up

Export Citation Format

Share Document