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@article{Johnson:2017:10.1073/pnas.1613786114,
author = {Johnson, S and Jones, NS},
doi = {10.1073/pnas.1613786114},
journal = {Proceedings of the National Academy of Sciences of USA},
pages = {5618--5623},
title = {Looplessness in networks is linked to trophic coherence},
url = {http://dx.doi.org/10.1073/pnas.1613786114},
volume = {114},
year = {2017}
}
TY - JOUR
AB - Many natural, complex systems are remarkably stable thanks to anabsence of feedback acting on their elements. When described as net-works, these exhibit few or no cycles, and associated matrices have smallleading 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 structuremight arise. We show here that the number of feedback loops in a net-work, as well as the eigenvalues of associated matrices, are determined bya structural property called trophic coherence, a measure of how neatlynodes fall into distinct levels. Our theory correctly classifies a variety ofnetworks – including those derived from genes, metabolites, species, neu-rons, words, computers and trading nations – into two distinct regimesof 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 worksuggests that the reasons for ‘looplessness’ in nature should be sought incoherence-inducing mechanisms.
AU - Johnson,S
AU - Jones,NS
DO - 10.1073/pnas.1613786114
EP - 5623
PY - 2017///
SN - 0027-8424
SP - 5618
TI - Looplessness in networks is linked to trophic coherence
T2 - Proceedings of the National Academy of Sciences of USA
UR - http://dx.doi.org/10.1073/pnas.1613786114
UR - http://hdl.handle.net/10044/1/48185
VL - 114
ER -