dorsal/arxiv
View SchemaSize reduction of complex networks preserving modularity
| Authors | A. Arenas, J. Duch, A. Fernandez, S. Gomez |
|---|---|
| Categories | |
| ArXiv ID | physics/0702015 |
| URL | https://arxiv.org/abs/physics/0702015 |
| DOI | 10.1088/1367-2630/9/6/176 |
| Journal | New Journal of Physics 9 (2007) 176 |
Abstract
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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"abstract": "The ubiquity of modular structure in real-world complex networks is being the\nfocus of attention in many trials to understand the interplay between network\ntopology and functionality. The best approaches to the identification of\nmodular structure are based on the optimization of a quality function known as\nmodularity. However this optimization is a hard task provided that the\ncomputational complexity of the problem is in the NP-hard class. Here we\npropose an exact method for reducing the size of weighted (directed and\nundirected) complex networks while maintaining invariant its modularity. This\nsize reduction allows the heuristic algorithms that optimize modularity for a\nbetter exploration of the modularity landscape. We compare the modularity\nobtained in several real complex-networks by using the Extremal Optimization\nalgorithm, before and after the size reduction, showing the improvement\nobtained. We speculate that the proposed analytical size reduction could be\nextended to an exact coarse graining of the network in the scope of real-space\nrenormalization.",
"arxiv_id": "physics/0702015",
"authors": [
"A. Arenas",
"J. Duch",
"A. Fernandez",
"S. Gomez"
],
"categories": [
"physics.comp-ph",
"cond-mat.other",
"cs.DM",
"physics.data-an",
"q-bio.QM"
],
"doi": "10.1088/1367-2630/9/6/176",
"journal_ref": "New Journal of Physics 9 (2007) 176",
"title": "Size reduction of complex networks preserving modularity",
"url": "https://arxiv.org/abs/physics/0702015"
},
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