The Evolution of Complex Networks: A New Framework

Details The Evolution of Complex Networks: A New Framework The Evolution of Complex Networks: A New Framework

2012-03-06

arxiv.org/abs/1203.1349v1

Physics

Physics and Society

4 pages and 2 figures

Scientific paper

We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical evidence that in many real networks there is a subset of "dominant edges" that control a major share of the total weight of the network. Furthermore, we introduce a new statistical procedure to study the evolution of networks over time, assessing if a given instance of the nework is taken at its steady state or not. Our results are quite general, since they are not based on a particular probability distribution or functional form of the weights. We test our model in the context of the International Trade Network, showing the existence of a core of dominant links and determining its size.

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