title: Deciphering the global organization of clustering in real complex networks.
abstract: We uncover the global organization of clustering in real complex networks. To this end, we ask whether triangles in real networks organize as in maximally random graphs with given degree and clustering distributions, or as in maximally ordered graph models where triangles are forced into modules. The answer comes by way of exploring m-core landscapes, where the m-core is defined, akin to the k-core, as the maximal subgraph with edges participating in at least m triangles. This property defines a set of nested subgraphs that, contrarily to k-cores, is able to distinguish between hierarchical and modular architectures. We find that the clustering organization in real networks is neither completely random nor ordered although, surprisingly, it is more random than modular. This supports the idea that the structure of real networks may in fact be the outcome of self-organized processes based on local optimization rules, in contrast to global optimization principles.
authors: Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain.
authors: Pol
authors: P
authors: Colomer-de-Simón
authors: M Ángeles
authors: MÁ
authors: Serrano
authors: Mariano G
authors: MG
authors: Beiró
authors: J Ignacio
authors: JI
authors: Alvarez-Hamelin
authors: Marián
authors: M
authors: Boguñá
mesh_terms: D016000:Cluster Analysis; D003198:Computer Simulation; D015233:Models, Statistical
references: Nature. 1998 Jun 4;393(6684):440-2
references: 9623998
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):020901
references: 19792067
references: Nature. 2012 Sep 27;489(7417):537-40
references: 22972194
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046121
references: 19905404
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5 Pt 2):056114
references: 17279975
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):066114
references: 20866485
references: Phys Rev Lett. 2006 Feb 3;96(4):040601
references: 16486798
references: Science. 1999 Oct 15;286(5439):509-12
references: 10521342
references: Phys Rev Lett. 2006 Aug 25;97(8):088701
references: 17026339
references: Science. 2002 Oct 25;298(5594):824-7
references: 12399590
references: Science. 2002 May 3;296(5569):910-3
references: 11988575
references: Phys Rev Lett. 2009 Jul 31;103(5):058701
references: 19792540
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036106
references: 21230138
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 2):066117
references: 15697444
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 2):046115
references: 20481794
references: Proc Natl Acad Sci U S A. 2004 Mar 2;101(9):2658-63
references: 14981240
references: Nat Commun. 2010 Sep 07;1:62
references: 20842196
references: Theor Popul Biol. 2007 Mar;71(2):160-73
references: 17222879
references: Phys Rev Lett. 2008 Feb 22;100(7):078701
references: 18352602
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5 Pt 2):056115
references: 17279976
references: Mol Biosyst. 2012 Mar;8(3):843-50
references: 22228307
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 2):066117
references: 22304165
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 2):036112
references: 21517563
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Dec;82(6 Pt 2):066118
references: 21230716
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Nov;70(5 Pt 2):056122
references: 15600707
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 2):036107
references: 19905180