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Universal Properties of Growing Networks

P. L. Krapivsky·B. Derrida
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Abstract

Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the non-percolating phase. The percolation transition is continuous but of infinite order and the size of the giant component is infinitely differentiable at the transition (though of course non-analytic). At the transition the average cluster size (of the finite components) is discontinuous.

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P. L. Krapivsky, B. Derrida. 2004-08-09. Universal Properties of Growing Networks. https://doi.org/10.1016/j.physa.2004.05.020

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