We study three special cases of simple generalized collaboration networks， namely the preferential attachment, random attachment and mixed attachment networks. Based on Markov chain theory, we provide a rigorous proof for the existence of the steady-state degree distribution of the network generated by this model and obtain its corresponding exact formula. In particular, for mixed attachment, if it has preferential attachment, degree distribution of the network obeys power-law distribution, and it is a scale-free network.
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