Size reduction of complex networks preserving modularity
Abstract
The ubiquity of modular structure in realworld complex networks is 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 nondeterministic polynomialtime hard (NPhard) class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining their modularity. This size reduction allows use of heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complexnetworks 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 realspace renormalization.
 Publication:

New Journal of Physics
 Pub Date:
 June 2007
 DOI:
 10.1088/13672630/9/6/176
 arXiv:
 arXiv:physics/0702015
 Bibcode:
 2007NJPh....9..176A
 Keywords:

 Physics  Computational Physics;
 Condensed Matter  Other;
 Computer Science  Discrete Mathematics;
 Physics  Data Analysis;
 Statistics and Probability;
 Quantitative Biology  Quantitative Methods
 EPrint:
 14 pages, 2 figures