Title: The Diverse Club: The Integrative Core of Complex 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.