Dynamics of condensation in growing complex networks

TL;DR

This paper investigates the dynamic process of condensation in growing networks with preferential attachment, revealing how a single node can dominate over time and how the process slows down near critical points.

Contribution

It characterizes the dynamics of condensation in fitness-based networks and shows the slow-down and emergence of a dominant node over long timescales.

Findings

Condensation dynamics slow down below the critical temperature.

A single node can dominate the network for extended periods.

Characteristic time diverges at critical points and zero temperature.

Abstract

A condensation transition was predicted for growing technological networks evolving by preferential attachment and competing quality of their nodes, as described by the fitness model. When this condensation occurs a node acquires a finite fraction of all the links of the network. Earlier studies based on steady state degree distribution and on the mapping to Bose-Einstein condensation, were able to identify the critical point. Here we characterize the dynamics of condensation and we present evidence that below the condensation temperature there is a slow down of the dynamics and that a single node (not necessarily the best node in the network) emerges as the winner for very long times. The characteristic time t* at which this phenomenon occurs diverges both at the critical point and at $T -> 0$ when new links are attached deterministically to the highest quality node of the network.