Network Evolution Based on Centrality

TL;DR

This paper investigates how network structures evolve when links are created or decay based on node centrality, revealing analytical solutions, phase transitions, and resulting degree distributions.

Contribution

It introduces a unified framework showing that various centrality measures lead to similar network dynamics and analytically characterizes the evolution process.

Findings

Network evolution exhibits nestedness with neighborhoods contained within higher-degree nodes.

A discontinuous transition occurs between hierarchical and homogeneous networks based on link decay rate.

The evolution mechanism produces double power-law degree distributions with related exponents.

Abstract

We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and solve analytically the network evolution. During the complete evolution, the network is characterized by nestedness: the neighbourhood of a node is contained in the neighbourhood of the nodes with larger degree. We find a discontinuous transition in the network density between hierarchical and homogeneous networks, depending on the rate of link decay. We also show that this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.