# Geometric explanation of the rich-club phenomenon in complex networks

## TL;DR

This paper introduces a geometry-based model that explains the rich-club phenomenon in complex networks, allowing for realistic generation of networks with diverse rich-club structures by adjusting a single parameter.

## Contribution

The paper presents a novel geometric growing model that can produce complex networks with realistic and diverse rich-club organizations, filling a gap in existing modeling approaches.

## Key findings

- Model accurately reproduces rich-club structures in real networks
- Adjusting one geometric parameter controls rich-club diversity
- Validated against Internet, protein, airport, and power grid networks

## Abstract

The rich club organization (the presence of highly connected hub core in a network) influences many structural and functional characteristics of networks including topology, the efficiency of paths and distribution of load. Despite its major role, the literature contains only a very limited set of models capable of generating networks with realistic rich club structure. One possible reason is that the rich club organization is a divisive property among complex networks which exhibit great diversity, in contrast to other metrics (e.g. diameter, clustering or degree distribution) which seem to behave very similarly across many networks. Here we propose a simple yet powerful geometry-based growing model which can generate realistic complex networks with high rich club diversity by controlling a single geometric parameter. The growing model is validated against the Internet, protein-protein interaction, airport and power grid networks.