Source-linked AI summary
Prominence and control: The weighted rich-club effect
Tore Opsahl, Vittoria Colizza, Pietro Panzarasa, Jose J. Ramasco
TL;DR
The paper asks whether prominent elements exchange disproportionately large amounts of resources among themselves, beyond what topology alone reveals. It introduces a weighted rich-club framework with comparable null models and applies it to transportation, scientific collaboration, and online communication, finding that prominence definitions expose different organizing patterns.
Problem
Existing rich-club analyses detect links among prominent nodes but neglect link weights, leaving their control over circulating resources largely unexplored.
Method
The framework ranks nodes by richness, measures the resources exchanged within increasingly selective clubs relative to the strongest possible links, and compares the result with null models preserving key network distributions.
Results
Weighted rich-club effects differ by prominence definition: strength reveals preferential exchange among prominent nodes across the studied networks, while degree-based results vary by domain.
Takeaways & Limitations
Weighted analysis uncovers organizing principles that topological assessment can miss, while varying prominence reveals multiple layers of system organization.
Takeaways & Limitations
A high weighted rich-club value alone does not establish a rich-node tendency, because randomly established networks can also produce nonzero values; appropriate null-model comparison is required.
Abstract
from arXiv · showhide
Complex systems are often characterized by large-scale hierarchical organizations. Whether the prominent elements, at the top of the hierarchy, share and control resources or avoid one another lies at the heart of a system's global organization and functioning. Inspired by network perspectives, we propose a new general framework for studying the tendency of prominent elements to form clubs with exclusive control over the majority of a system's resources. We explore associations between prominence and control in the fields of transportation, scientific collaboration, and online communication.