eprintid: 2818
rev_number: 10
eprint_status: archive
userid: 69
dir: disk0/00/00/28/18
datestamp: 2015-11-05 11:58:38
lastmod: 2018-03-08 17:02:35
status_changed: 2015-11-05 11:58:38
type: article
metadata_visibility: show
creators_name: Squartini, Tiziano
creators_name: Picciolo, Francesco
creators_name: Ruzzenenti, Franco
creators_name: Garlaschelli, Diego
creators_id: tiziano.squartini@imtlucca.it
creators_id: 
creators_id: 
creators_id: diego.garlaschelli@imtlucca.it
title: Reciprocity of weighted networks
ispublished: pub
subjects: HA
subjects: QA
subjects: QC
divisions: EIC
full_text_status: public
keywords: Applied physics, Complex networks, Information theory and computation, Statistics
abstract: In directed networks, reciprocal links have dramatic effects on dynamical processes, network growth, and higher-order structures such as motifs and communities. While the reciprocity of binary networks has been extensively studied, that of weighted networks is still poorly understood, implying an ever-increasing gap between the availability of weighted network data and our understanding of their dyadic properties. Here we introduce a general approach to the reciprocity of weighted networks, and define quantities and null models that consistently capture empirical reciprocity patterns at different structural levels. We show that, counter-intuitively, previous reciprocity measures based on the similarity of mutual weights are uninformative. By contrast, our measures allow to consistently classify different weighted networks according to their reciprocity, track the evolution of a network's reciprocity over time, identify patterns at the level of dyads and vertices, and distinguish the effects of flux (im)balances or other (a)symmetries from a true tendency towards (anti-)reciprocation.
date: 2013
date_type: published
publication: Scientific Reports
volume: 3
number: 2729
publisher: Nature Publishing Group
id_number: 10.1038/srep02729
refereed: TRUE
issn: 2045-2322
official_url: http://www.nature.com/articles/srep02729#comments
citation:   Squartini, Tiziano and Picciolo, Francesco and Ruzzenenti, Franco and Garlaschelli, Diego  Reciprocity of weighted networks.  Scientific Reports, 3 (2729).   ISSN 2045-2322      (2013)  
document_url: http://eprints.imtlucca.it/2818/1/srep02729.pdf