Marc Barthélemy and Alessandro Flammini J. Stat. Mech. (2006) L07002 doi:10.1088/1742-5468/2006/07/L07002
Marc Barthélemy1,2 and Alessandro Flammini1
Show affiliationsInspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.
89.75.Hc Networks and genealogical trees
Issue 07 (July 2006)
Received 29 March 2006, accepted for publication 10 July 2006
Published 24 July 2006
Marc Barthélemy and Alessandro Flammini J. Stat. Mech. (2006) L07002
Piotr Cieplak et al 2009 J. Phys.: Condens. Matter 21 333102
F Acernese et al 2008 Class. Quantum Grav. 25 205007
J E Avron et al 2005 New J. Phys. 7 234
Louis H Kauffman and Samuel J Lomonaco Jr 2004 New J. Phys. 6 134
Claudius Gros 2007 New J. Phys. 9 109
P A Hiskett et al 2006 New J. Phys. 8 193
E A Viktorov et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 L9
Michael Lam and Martin Mintchev 2009 Physiol. Meas. 30 763
M V Berry 2002 New J. Phys. 4 66