The Diverse Club: The Integrative Core of Complex Networks

TL;DR

This paper identifies a new type of node group called the diverse club in complex networks, which supports global integration more effectively than the traditionally studied rich club, across various biological and man-made systems.

Contribution

The study introduces the concept of the diverse club, demonstrates its prevalence across multiple networks, and presents a generative model showing its distinct evolutionary origins from the rich club.

Findings

The diverse club is more interconnected than the rich club.

Edges in the diverse club are more critical for network integration.

The diverse club is ubiquitous across biological and man-made networks.

Abstract

A complex system can be represented and analyzed as a network, where nodes represent the units of the network and edges represent connections between those units. For example, a brain network represents neurons as nodes and axons between neurons as edges. In many networks, some nodes have a disproportionately high number of edges. These nodes also have many edges between each other, and are referred to as the rich club. In many different networks, the nodes of this club are assumed to support global network integration. However, another set of nodes potentially exhibits a connectivity structure that is more advantageous to global network integration. Here, in a myriad of different biological and man-made networks, we discover the diverse club--a set of nodes that have edges diversely distributed across the network. The diverse club exhibits, to a greater extent than the rich club, properties consistent with an integrative network function--these nodes are more highly interconnected and their edges are more critical for efficient global integration. Moreover, we present a generative evolutionary network model that produces networks with a diverse club but not a rich club, thus demonstrating that these two clubs potentially evolved via distinct selection pressures. Given the variety of different networks that we analyzed--the c. elegans, the macaque brain, the human brain, the United States power grid, and global air traffic--the diverse club appears to be ubiquitous in complex networks. These results warrant the distinction and analysis of two critical clubs of nodes in all complex systems.