eprintid: 2792
rev_number: 6
eprint_status: archive
userid: 69
dir: disk0/00/00/27/92
datestamp: 2015-11-02 13:32:38
lastmod: 2015-11-02 13:32:38
status_changed: 2015-11-02 13:32:38
type: article
succeeds: 2685
metadata_visibility: show
creators_name: Borassi, Michele
creators_name: Chessa, Alessandro
creators_name: Caldarelli, Guido
creators_id: 
creators_id: alessandro.chessa@imtlucca.it
creators_id: guido.caldarelli@imtlucca.it
title: Hyperbolicity measures democracy in real-world networks
ispublished: pub
subjects: HA
subjects: HM
subjects: QC
divisions: EIC
full_text_status: none
monograph_type: working_paper
abstract: In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is “aristocratic”, since few elements “connect” the system, while a non-hyperbolic network has a more “democratic” structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an “influence area” for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define “local” networks (i.e., social or peer-to-peer networks), and large in “global” networks (i.e., power grid, metabolic networks, or autonomous system networks).
date: 2015
date_type: published
publication: Physical Review E
volume: 92
number: 3
publisher: American Physical Society
pagerange: 032812
pages: 10
id_number: 10.1103/PhysRevE.92.032812
institution: IMT Institute for Advanced Studies Lucca
refereed: TRUE
issn: 1539-3755
official_url: http://arxiv.org/abs/1503.03061
citation:   Borassi, Michele and Chessa, Alessandro and Caldarelli, Guido  Hyperbolicity measures democracy in real-world networks.  Physical Review E, 92 (3).  032812.  ISSN 1539-3755      (2015)