Phase Transition on The Degree Sequence of a Mixed Random Graph Process

Details Phase Transition on The Degree Sequence of a Mixed Random Graph Process Phase Transition on The Degree Sequence of a Mixed Random Graph Process

2008-07-17

arxiv.org/abs/0807.2811v4

Mathematics

Probability

24 pages

Scientific paper

This paper focuses on the problem of the degree sequence for a mixed random graph process which continuously combines the {\it classical} model and the BA model. Note that the number of step added edges for the mixed model is random and non-uniformly bounded. By developing a comparing argument, phase transition on the degree distributions of the mixed model is revealed: while the {\it pure} classical model possesses a {\it exponential} degree sequence, the {\it pure} BA model and the mixed model possess {\it power law} degree sequences. As an application of the methodology, phase transition on the degree sequence of {\it another} mixed model with {\it hard copying} is also studied, especially, in the power law region, the inverse power can take any value greater than 1.

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