Applying clique-decomposition for computing Gromov hyperbolicity - Archive ouverte HAL Access content directly
Journal Articles Theoretical Computer Science Year : 2017

Applying clique-decomposition for computing Gromov hyperbolicity

(1) , (2) , (2) , (3)
1
2
3

Abstract

Given a graph, its hyperbolicity is a measure of how close its distance distribution is to the one of a tree. This parameter has gained recent attention in the analysis of some graph algorithms and the classification of complex networks. We study on practical improvements for the computation of hyperbolicity in large graphs. Precisely, we investigate on relations between the hyperbolicity of a graph G and the hyperbolicity of its atoms, that are the subgraphs output by the clique-decomposition invented by Tarjan [51, 65]. We prove that the maximum hyperbolicity taken over the atoms is at most one unit off from the hyperbol-icity of G and the bound is sharp. We also give an algorithm to slightly modify the atoms, called the " substitution method " , which is at no extra cost than computing the clique-decomposition, and so that the maximum hyperbolicity taken over the resulting graphs is exactly the hyperbolicity of the input graph G. An experimental evaluation of our method for computing the hyperbolicity of a given graph from its atoms is provided for collaboration networks and biological networks. Finally, on a more theoretical side, we deduce from our results the first linear-time algorithm for computing the hyperbolicity of an outerplanar graph.
Fichier principal
Vignette du fichier
CCDL-2017.pdf (1.23 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01540756 , version 1 (16-06-2017)

Identifiers

Cite

Nathann Cohen, David Coudert, Guillaume Ducoffe, Aurélien Lancin. Applying clique-decomposition for computing Gromov hyperbolicity. Theoretical Computer Science, 2017, 690, pp.114-139. ⟨10.1016/j.tcs.2017.06.001⟩. ⟨hal-01540756⟩
369 View
281 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More