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  Impact of single links in competitive percolation

Nagler, J., Levina, A., & Timme, M. (2011). Impact of single links in competitive percolation. Nature Physics, 7(3), 265-270. doi:10.1038/NPHYS1860.

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https://www.nature.com/articles/nphys1860.pdf (Publisher version)
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Nagler, J, Author
Levina, A1, Author              
Timme, M, Author
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1External Organizations, ou_persistent22              

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 Abstract: How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of ‘explosive percolation’ suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single-link additions. We show that in generic competitive percolation processes, including those showing explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce substantial gaps, because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively.

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Language(s): eng - English
 Dates: 2011-01
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: DOI: 10.1038/NPHYS1860
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Title: Nature Physics
  Other : Nat. Phys.
Source Genre: Journal
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Publ. Info: London : Nature Pub. Group
Pages: - Volume / Issue: 7 (3) Sequence Number: - Start / End Page: 265 - 270 Identifier: ISSN: 1745-2473
CoNE: https://pure.mpg.de/cone/journals/resource/1000000000025850