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Looplessness in networks is linked to trophic coherence

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Title: Looplessness in networks is linked to trophic coherence
Authors: Johnson, S
Jones, NS
Item Type: Journal Article
Abstract: Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as net- works, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been suggested that this architecture can con- fer advantages to the system as a whole, such as ‘qualitative stability’, but this observation does not in itself explain how a loopless structure might arise. We show here that the number of feedback loops in a net- work, as well as the eigenvalues of associated matrices, are determined by a structural property called trophic coherence, a measure of how neatly nodes fall into distinct levels. Our theory correctly classifies a variety of networks – including those derived from genes, metabolites, species, neu- rons, words, computers and trading nations – into two distinct regimes of high and low feedback, and provides a null model to gauge the signifi- cance of related magnitudes. Since trophic coherence suppresses feedback, whereas an absence of feedback alone does not lead to coherence, our work suggests that the reasons for ‘looplessness’ in nature should be sought in coherence-inducing mechanisms.
Issue Date: 30-May-2017
Date of Acceptance: 17-Apr-2017
URI: http://hdl.handle.net/10044/1/48185
DOI: 10.1073/pnas.1613786114
ISSN: 0027-8424
Publisher: National Academy of Sciences
Start Page: 5618
End Page: 5623
Journal / Book Title: Proceedings of the National Academy of Sciences of USA
Volume: 114
Issue: 22
Copyright Statement: © 2017 National Academy of Sciences
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
Funder's Grant Number: EP/N014529/1
276454
Keywords: Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
networks
stability
feedback
trophic coherence
food webs
FOOD WEBS
COMPLEX NETWORKS
RANDOM GRAPHS
STABILITY
feedback
food webs
networks
stability
trophic coherence
physics.soc-ph
physics.soc-ph
Publication Status: Published
Open Access location: https://arxiv.org/abs/1505.07332
Online Publication Date: 2017-05-16
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences