Size reduction of complex networks preserving modularity

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The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity ... continued below

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Arenas, A.; Duch, J.; Fernandez, A. & Gomez, S. December 24, 2008.

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The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.

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  • Journal Name: New Journal of Physics

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  • Report No.: LBNL-1444E
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1088/1367-2630/10/5/053039 | External Link
  • Office of Scientific & Technical Information Report Number: 946812
  • Archival Resource Key: ark:/67531/metadc893339

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  • December 24, 2008

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:10 p.m.

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Arenas, A.; Duch, J.; Fernandez, A. & Gomez, S. Size reduction of complex networks preserving modularity, article, December 24, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc893339/: accessed September 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.