Optimal map of the modular structure of complex networks

A. Arenas, J. Borge-Holthoefer, S. Gómez, G. Zamora-López

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

The modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and the function of complex systems. Generally speaking, modules are islands of highly connected nodes separated by a relatively small number of links. Every module can have the contributions of links from any node in the network. The challenge is to disentangle these contributions to understand how the modular structure is built. The main problem is that the analysis of a certain partition into modules involves, in principle, as much data as the number of modules times the number of nodes. To confront this challenge, here we first define the contribution matrix, the mathematical object containing all the information about the partition of interest, and then we use truncated singular value decomposition to extract the best representation of this matrix in a plane. The analysis of this projection allows us to scrutinize the skeleton of the modular structure, revealing the structure of individual modules and their interrelations.

Original languageEnglish
Article number053009
JournalNew Journal of Physics
Volume12
DOIs
Publication statusPublished - 6 May 2010
Externally publishedYes

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modules
partitions
matrices
complex systems
musculoskeletal system
projection
decomposition
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Arenas, A., Borge-Holthoefer, J., Gómez, S., & Zamora-López, G. (2010). Optimal map of the modular structure of complex networks. New Journal of Physics, 12, [053009]. https://doi.org/10.1088/1367-2630/12/5/053009

Optimal map of the modular structure of complex networks. / Arenas, A.; Borge-Holthoefer, J.; Gómez, S.; Zamora-López, G.

In: New Journal of Physics, Vol. 12, 053009, 06.05.2010.

Research output: Contribution to journalArticle

Arenas, A, Borge-Holthoefer, J, Gómez, S & Zamora-López, G 2010, 'Optimal map of the modular structure of complex networks', New Journal of Physics, vol. 12, 053009. https://doi.org/10.1088/1367-2630/12/5/053009
Arenas A, Borge-Holthoefer J, Gómez S, Zamora-López G. Optimal map of the modular structure of complex networks. New Journal of Physics. 2010 May 6;12. 053009. https://doi.org/10.1088/1367-2630/12/5/053009
Arenas, A. ; Borge-Holthoefer, J. ; Gómez, S. ; Zamora-López, G. / Optimal map of the modular structure of complex networks. In: New Journal of Physics. 2010 ; Vol. 12.
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