Abstract
The modular structure of a complex network is an important and well-studied topological property. Within this modular framework, particular nodes which play key roles have been previously identified based on the node’s degree, and on the node’s participation coefficient, a measure of the diversity of a node’s intermodular connections. In this contribution, we develop a generalization of the participation coefficient, called the gateway coefficient, which measures not only the diversity of the intermodular connections, but also how critical these connections are to intermodular connectivity; in brief, nodes which form rare or unique “gateways” between sparsely connected modules rank highly in this measure. We illustrate the use of the gateway coefficient with simulated networks with defined modular structure, as well as networks obtained from air transportation data and functional neuroimaging.
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References
S.H. Strogatz, Nature 410, 268 (2001)
D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)
M. Newman, Phys. Rev. E 64, 2001 (2001)
E. Bullmore, O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009)
M. Girvan, M.E.J. Newman, Proc. Natl. Acad. Sci. USA 99, 7821 (2002)
M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004)
R. Guimerà, M. Sales-Pardo, L.A.N. Amaral, Phys. Rev. E 76, 036102 (2007)
S. Shai et al., arXiv:1404.4748 (2014)
F. Bartolomei et al., Ann. Neurol. 59, 128 (2006)
D. Bassett et al., J. Neurosci. 28, 9239 (2008)
C. Stam et al., Brain 132, 213 (2009)
M.W. Cho, M.Y. Choi, Int. J. Imaging Syst. Technol. 20, 108 (2010)
A. Barrat et al., Proc. Natl. Acad. Sci. USA 101, 3747 (2004)
R. Guimerà et al., Proc. Natl. Acad. Sci. USA 102, 7794 (2005)
R. Cohen et al., Phys. Rev. Lett. 86, 3682 (2001)
R. Guimerà, L.A.N. Amaral, Nature 433, 895 (2005)
R.A. McFarland, Human Factors in Air Transportation: Occupational Health and Safety (McGraw-Hill Book Co., 1953)
S.G. Britton, Ann. Tourism Res. 9, 331 (1982)
K. Button, S. Taylor, J. Air. Transp. Manag. 6, 209 (2000)
E. Bullmore, O. Sporns, Nat. Rev. Neurosci. 13, 336 (2012)
O. Sporns, C.J. Honey, R. Kötter, PLoS One 2, 10 (2007)
S. Achard, E. Bullmore, PLoS Comput. Biol. 3, 2 (2007)
Y.N. Kenett et al., PLoS One 6, e23912 (2011)
M.A. Castro et al., Genome Biology 13, R29 (2012)
A.-L. Barabási, R. Albert, Science 286, 509 (1999)
L. Amaral et al., Proc. Natl. Acad. Sci. USA 97, 11149 (2000)
S.G. Greening, E.C. Finger, D.G.V. Mitchell, NeuroImage 54, 1432 (2011)
B. Zhang, S. Horvath, Stat. Appl. Genet. Mol. Biol. 4, 17 (2005)
R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna (2008), http://www.R-project.org
E. Ruiz Vargas et al., Physica A 405, 151 (2014)
E. Ravasz et al., Science 297, 1551 (2002)
P. Langfelder, Z. Bin, S. Horvath, Bioinformatics 24, 719 (2008)
J. Talairach, P. Tournoux, Co-Planar stereotaxic atlas of the human brain: 3-D proportional system: An approach to cerebral imaging (Thieme, 1988)
S. Arroyo et al., Epilepsia 38, 600 (1997)
S.L. Thompson-Schill, M. D’Esposito, I.P. Kan, Neuron 23, 513 (1999)
S.M. Kosslyn et al., Science 284, 167 (1999)
A. Bechara, Nat. Neurosci. 8, 1458 (2005)
C.D. Chambers et al., Nat. Neurosci. 7, 217 (2004)
M.E. Raichle et al., Proc. Natl. Acad. Sci. USA 98, 676 (2001)
L.A.N. Amaral et al., Proc. Natl. Acad. Sci. USA 97, 11149 (2000)
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Ruiz Vargas, E., Wahl, L. The gateway coefficient: a novel metric for identifying critical connections in modular networks. Eur. Phys. J. B 87, 161 (2014). https://doi.org/10.1140/epjb/e2014-40800-7
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DOI: https://doi.org/10.1140/epjb/e2014-40800-7