2008/02/29 by M. Angeles Serrano, M. Ángeles Serrano · 2 citations
Agricultural and Biological Sciences · Mathematics · Physics and Astronomy · #Artificial intelligence #Club #Cohesion (chemistry) #Complex Network Analysis Techniques #Complex network #Computer science #Contrast (vision) #Geology #Mathematics #Network structure #Normalization (sociology) #Opinion Dynamics and Social Influence #Physics #Plant and animal studies #Sociology #Theoretical computer science #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.78.026101
published as PHYSICAL REVIEW E 78, 026101 (2008) · 12 pages, 2 figures
arxiv created 2008/05/14 · openalex publication_date 2008/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.