Accelerated growth of networks

TL;DR

This paper investigates how accelerated growth in networks affects their structure, connection distribution, and dynamics, with applications to language networks and societal wealth distribution.

Contribution

It introduces models of accelerated network growth and demonstrates their relevance to real-world networks like the Word Web and societal wealth condensation.

Findings

Accelerated growth influences network connection distribution.

Models explain the structure of the Word Web.

Accelerated growth relates to wealth condensation in societies.

Abstract

In many real growing networks the mean number of connections per vertex increases with time. The Internet, the Word Wide Web, collaboration networks, and many others display this behavior. Such a growth can be called {\em accelerated}. We show that this acceleration influences distribution of connections and may determine the structure of a network. We discuss general consequences of the acceleration and demonstrate its features applying simple illustrating examples. In particular, we show that the accelerated growth fairly well explains the structure of the Word Web (the network of interacting words of human language). Also, we use the models of the accelerated growth of networks to describe a wealth condensation transition in evolving societies.