relation: http://eprints.imtlucca.it/2827/
title: Unbiased sampling of network ensembles
creator: Squartini, Tiziano
creator: Mastrandrea, Rossana
creator: Garlaschelli, Diego
subject: QA Mathematics
subject: QC Physics
description: Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the sampling process is unbiased and efficient. The main approaches are microcanonical, i.e. they sample graphs that match the enforced constraints exactly. Unfortunately, when applied to strongly heterogeneous networks (like most real-world examples), the majority of these approaches become biased and/or time-consuming. Moreover, the algorithms defined in the simplest cases, such as binary graphs with given degrees, are not easily generalizable to more complicated ensembles. Here we propose a solution to the problem via the introduction of a ‘Maximize and Sample’ (‘Max & Sam’ for short) method to correctly sample ensembles of networks where the constraints are ‘soft’, i.e. realized as ensemble averages. Our method is based on exact maximum-entropy distributions and is therefore unbiased by construction, even for strongly heterogeneous networks. It is also more computationally efficient than most microcanonical alternatives. Finally, it works for both binary and weighted networks with a variety of constraints, including combined degree-strength sequences and full reciprocity structure, for which no alternative method exists. Our canonical approach can in principle be turned into an unbiased microcanonical one, via a restriction to the relevant subset. Importantly, the analysis of the fluctuations of the constraints suggests that the microcanonical and canonical versions of all the ensembles considered here are not equivalent. We show various real-world applications and provide a code implementing all our algorithms.
publisher: IOPscience
date: 2015
type: Article
type: PeerReviewed
format: application/pdf
language: en
rights: cc_by_nc
identifier: http://eprints.imtlucca.it/2827/1/pdf%20%282%29.pdf
identifier:   Squartini, Tiziano and Mastrandrea, Rossana and Garlaschelli, Diego  Unbiased sampling of network ensembles.  New Journal of Physics, 17 (2).  023052.  ISSN 1367-2630      (2015)  
relation: http://stacks.iop.org/1367-2630/17/i=2/a=023052
relation: 10.1088/1367-2630/17/2/023052