Low-rank network decomposition reveals structural characteristics of small-world networks

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Victor J BarrancaDavid Cai

Abstract

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering and regularity of network connections. While many existing network characterizations rely on constructing benchmark networks for comparison or fail to describe the structural properties of relatively densely connected networks, our classification relies only on the intrinsic network structure and is quite robust with respect to changes in connection density, producing stable results across network realizations. Using this framework, we analyze several real-wo...Continue Reading

References

Jun 12, 1998·Nature·D J Watts, S H Strogatz
Oct 16, 1999·Science·A L Barabasi, R Albert
Sep 27, 2000·Proceedings of the National Academy of Sciences of the United States of America·L A AmaralH E Stanley
Oct 18, 2000·Nature·H JeongA L Barabási
Nov 3, 2001·Physical Review Letters·V Latora, M Marchiori
Dec 26, 2001·Proceedings. Biological Sciences·S N Dorogovtsev, J F Mendes
Jun 13, 2002·Proceedings of the National Academy of Sciences of the United States of America·M Girvan, M E J Newman
Mar 26, 2003·Microbes and Infection·Fredrik LiljerosLuis A Nunes Amaral
Oct 1, 2003·Proceedings of the National Academy of Sciences of the United States of America·Victor Spirin, Leonid A Mirny
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R GuimeràA Arenas
Jun 1, 2004·Physical Review Letters·Alex RoxinSara A Solla
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman
Sep 8, 2004·Trends in Cognitive Sciences·Olaf SpornsClaus C Hilgetag
Sep 17, 2004·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Theoden I NetoffJohn A White
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Aaron ClausetCristopher Moore
Apr 12, 2006·Physical Review Letters·Alex ArenasConrad J Pérez-Vicente
May 26, 2006·Proceedings of the National Academy of Sciences of the United States of America·M E J Newman
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M E J Newman
Nov 3, 2006·The Neuroscientist : a Review Journal Bringing Neurobiology, Neurology and Psychiatry·Danielle Smith Bassett, Ed Bullmore
Dec 13, 2006·Proceedings of the National Academy of Sciences of the United States of America·Olaf Sporns, Christopher J Honey
Dec 28, 2006·Proceedings of the National Academy of Sciences of the United States of America·Santo Fortunato, Marc Barthélemy
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan G RestrepoBrian R Hunt
Jun 4, 2008·Physical Review Letters·E A Leicht, M E J Newman
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Brian BallM E J Newman
Jan 4, 2012·IEEE Transactions on Pattern Analysis and Machine Intelligence·Yigang PengYi Ma
Jan 1, 2011·Brain Connectivity·Qawi K TelesfordPaul J Laurienti
Nov 12, 1986·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·J G WhiteS Brenner
Nov 2, 2013·Science·Nikola T MarkovHenry Kennedy
Jun 4, 2015·Scientific Reports·Victor J BarrancaDavid Cai

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Citations

Sep 27, 2018·Physical Review. E·Liliia Ziganurova, Lev N Shchur
Jan 21, 2019·Journal of Computational Neuroscience·Victor J BarrancaGenji Kawakita

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