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arXiv · 0804.1768

Dynamics of condensation in growing complex networks

Luca Ferretti·Ginestra Bianconi
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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.

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Luca Ferretti, Ginestra Bianconi. 2009-10-16. Dynamics of condensation in growing complex networks. https://doi.org/10.1103/physreve.78.056102

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