Random Graphs Associated to Some Discrete and Continuous Time Preferential Attachment Models

  title={Random Graphs Associated to Some Discrete and Continuous Time Preferential Attachment Models},
  author={Ang{\'e}lica Pach{\'o}n and Federico Polito and Laura Sacerdote},
  journal={Journal of Statistical Physics},
We give a common description of Simon, Barabási–Albert, II-PA and Price growth models, by introducing suitable random graph processes with preferential attachment mechanisms. Through the II-PA model, we prove the conditions for which the asymptotic degree distribution of the Barabási–Albert model coincides with the asymptotic in-degree distribution of the Simon model. Furthermore, we show that when the number of vertices in the Simon model (with parameter $$\alpha $$α) goes to infinity, a… 
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