Rich-club vs rich-multipolarization phenomena in weighted networks.

Large-scale hierarchies characterize complex networks in different domains. Elements at the top, usually the most central or influential, may show multipolarization or tend to club together, forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves the nodes' strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss the ability of the scanning of weighted subgraphs formed by the high-strength hubs to unveil features in contrast to the average: the formation of local alliances in multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for correct understanding of functionalities and dynamical processes relying on hub interconnectedness.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Marián Boguñá,et al.  Correlations in weighted networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Marián Boguñá,et al.  Self-similarity of complex networks and hidden metric spaces , 2007, Physical review letters.

[4]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[5]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[6]  Stefan Wuchty,et al.  Rich-Club Phenomenon in the Interactome of P. falciparum—Artifact or Signature of a Parasitic Life Style? , 2007, PloS one.

[7]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.

[9]  K. Gleditsch,et al.  Expanded Trade and GDP Data , 2002 .

[10]  Alessandro Vespignani,et al.  Detecting rich-club ordering in complex networks , 2006, physics/0602134.

[11]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Marián Boguñá,et al.  Topology of the world trade web. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Alessandro Vespignani,et al.  Cut-offs and finite size effects in scale-free networks , 2003, cond-mat/0311650.

[14]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  K. Kaski,et al.  The International Trade Network: weighted network analysis and modelling , 2007, 0707.4343.

[16]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.