Detecting rich-club ordering in complex networks

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue in understanding their fabric and dynamical properties1,2,3,4,5. The ‘rich-club’ phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities, and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences4,5,6,7,8. Here, we provide the analytical expression and the correct null models that allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.

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