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arXiv · 1312.7803

Choice-Driven Phase Transition in Complex Networks

P. L. Krapivsky·S. Redner
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Abstract

We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a new node attaches to the target with the highest degree. Depending on precise details of the attachment rule, the resulting networks has three possible outcomes: (i) a non-universal power-law degree distribution; (ii) a single macroscopic hub (a node whose degree is of the order of N, the number of network nodes), while the remainder of the nodes comprises a non-universal power-law degree distribution; (iii) a degree distribution that decays as (k ln k)^{-2} at the transition between cases (i) and (ii). These properties are robust when attachment occurs to the highest-degree node from at least two targets. When attachment is made to a target whose degree is not the highest, the degree distribution has the ultra-narrow double-exponential form exp(-const. x e^k), from which the largest degree grows only as ln(ln N).

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P. L. Krapivsky, S. Redner. 2014-03-24. Choice-Driven Phase Transition in Complex Networks. https://doi.org/10.1088/1742-5468%2F2014%2F04%2Fp04021

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