Hyperbolic representation learning: Revisiting and advancing
The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable
attention in the realm of representation learning. Current endeavors in hyperbolic …
attention in the realm of representation learning. Current endeavors in hyperbolic …
Tree-like structure in large social and information networks
AB Adcock, BD Sullivan… - 2013 IEEE 13th …, 2013 - ieeexplore.ieee.org
Although large social and information networks are often thought of as having hierarchical or
tree-like structure, this assumption is rarely tested. We have performed a detailed empirical …
tree-like structure, this assumption is rarely tested. We have performed a detailed empirical …
Better approximation algorithms for the graph diameter
The diameter is a fundamental graph parameter and its computation is necessary in many
applications. The fastest known way to compute the diameter exactly is to solve the All-Pairs …
applications. The fastest known way to compute the diameter exactly is to solve the All-Pairs …
On the hyperbolicity of small-world and treelike random graphs
Hyperbolicity is a property of a graph that may be viewed as a “soft” version of a tree, and
recent empirical and theoretical work has suggested that many graphs arising in Internet …
recent empirical and theoretical work has suggested that many graphs arising in Internet …
Tree! i am no tree! i am a low dimensional hyperbolic embedding
R Sonthalia, A Gilbert - Advances in Neural Information …, 2020 - proceedings.neurips.cc
Given data, finding a faithful low-dimensional hyperbolic embedding of the data is a key
method by which we can extract hierarchical information or learn representative geometric …
method by which we can extract hierarchical information or learn representative geometric …
Helly groups
J Chalopin, V Chepoi, A Genevois, H Hirai… - arXiv preprint arXiv …, 2020 - arxiv.org
Helly graphs are graphs in which every family of pairwise intersecting balls has a non-empty
intersection. This is a classical and widely studied class of graphs. In this article we focus on …
intersection. This is a classical and widely studied class of graphs. In this article we focus on …
Metric embedding, hyperbolic space, and social networks
We consider the problem of embedding an undirected graph into hyperbolic space with
minimum distortion. A fundamental problem in its own right, it has also drawn a great deal of …
minimum distortion. A fundamental problem in its own right, it has also drawn a great deal of …
Into the square: On the complexity of some quadratic-time solvable problems
M Borassi, P Crescenzi, M Habib - Electronic Notes in Theoretical …, 2016 - Elsevier
We analyze several quadratic-time solvable problems, and we show that these problems are
not solvable in truly subquadratic time (that is, in time O (n 2− ϵ) for some ϵ> 0), unless the …
not solvable in truly subquadratic time (that is, in time O (n 2− ϵ) for some ϵ> 0), unless the …
Hyperbolicities in CAT (0) cube complexes
A Genevois - L'Enseignement Mathématique, 2020 - ems.press
This paper is a survey dedicated to the following question: given a group acting on a CAT (0)
cube complex, how to exploit this action to determine whether or not the group is …
cube complex, how to exploit this action to determine whether or not the group is …
Metric tree‐like structures in real‐world networks: an empirical study
Based on solid theoretical foundations, we present strong evidence that a number of real‐
world networks, taken from different domains (such as Internet measurements, biological …
world networks, taken from different domains (such as Internet measurements, biological …