Dynamics of condensation in growing complex networks

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.

(4 pages,3 figures)

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Cited by in corpus (8)

• Complex Quantum Networks: a Topical Review
• Dynamics of condensation in the totally asymmetric inclusion process
• A k-deformed Model of Growing Complex Networks with Fitness
• Condensation and topological phase transitions in a dynamical network model with rewiring of the links
• Statistics of leaders and lead changes in growing networks
• Complex systems: features, similarity and connectivity
• Finite-time fluctuations in the degree statistics of growing networks
• On leaders and condensates in a growing network