Origins of fractality in the growth of complex networks

Chaoming Song; Shlomo Havlin; Hernán A. Makse

doi:10.1038/nphys266

Origins of fractality in the growth of complex networks

Chaoming Song
, Shlomo Havlin
, Hernán A. Makse

Department of Physics - at Bar-Ilan University

City University of New York

Research output: Contribution to journal › Article › peer-review

539 Scopus citations

Abstract

Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.

Original language	English
Pages (from-to)	275-281
Number of pages	7
Journal	Nature Physics
Volume	2
Issue number	4
DOIs	https://doi.org/10.1038/nphys266
State	Published - Apr 2006

Bibliographical note

Funding Information:
We would like to thank J. Brujić for illuminating discussions and E. Ravasz for providing the data on the metabolic network. S.H. wishes to thank the Israel Science Foundation, ONR and Dysonet for support. This work is supported by the National Science Foundation, DMR-0239504 to H.A.M. Correspondence and requests for materials should be addressed to H.A.M. Supplementary Information accompanies this paper on www.nature.com/naturephysics.

Funding

We would like to thank J. Brujić for illuminating discussions and E. Ravasz for providing the data on the metabolic network. S.H. wishes to thank the Israel Science Foundation, ONR and Dysonet for support. This work is supported by the National Science Foundation, DMR-0239504 to H.A.M. Correspondence and requests for materials should be addressed to H.A.M. Supplementary Information accompanies this paper on www.nature.com/naturephysics.

Funders	Funder number
National Science Foundation	DMR-0239504
Office of Naval Research
Israel Science Foundation

Access to Document

10.1038/nphys266

Cite this

@article{887d8ec7dbea427185a0c616bf943b36,

title = "Origins of fractality in the growth of complex networks",

abstract = "Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.",

author = "Chaoming Song and Shlomo Havlin and Makse, \{Hern{\'a}n A.\}",

note = "Funding Information: We would like to thank J. Bruji{\'c} for illuminating discussions and E. Ravasz for providing the data on the metabolic network. S.H. wishes to thank the Israel Science Foundation, ONR and Dysonet for support. This work is supported by the National Science Foundation, DMR-0239504 to H.A.M. Correspondence and requests for materials should be addressed to H.A.M. Supplementary Information accompanies this paper on www.nature.com/naturephysics.",

year = "2006",

month = apr,

doi = "10.1038/nphys266",

language = "אנגלית",

volume = "2",

pages = "275--281",

journal = "Nature Physics",

issn = "1745-2473",

publisher = "Nature Research",

number = "4",

}

TY - JOUR

T1 - Origins of fractality in the growth of complex networks

AU - Song, Chaoming

AU - Havlin, Shlomo

AU - Makse, Hernán A.

N1 - Funding Information: We would like to thank J. Brujić for illuminating discussions and E. Ravasz for providing the data on the metabolic network. S.H. wishes to thank the Israel Science Foundation, ONR and Dysonet for support. This work is supported by the National Science Foundation, DMR-0239504 to H.A.M. Correspondence and requests for materials should be addressed to H.A.M. Supplementary Information accompanies this paper on www.nature.com/naturephysics.

PY - 2006/4

Y1 - 2006/4

N2 - Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.

AB - Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective 'repulsion' (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.

UR - https://www.scopus.com/pages/publications/33645780366

U2 - 10.1038/nphys266

DO - 10.1038/nphys266

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33645780366

SN - 1745-2473

VL - 2

SP - 275

EP - 281

JO - Nature Physics

JF - Nature Physics

IS - 4

ER -

Origins of fractality in the growth of complex networks

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this