Open AccessThe degree distribution of simple generalized collaboration networks
Author(s) -
Qianchuan Zhao,
Xianglong Kong,
Zhixiang Hou
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.6682
Subject(s) - preferential attachment , degree distribution , degree (music) , simple (philosophy) , scale free network , markov chain , distribution (mathematics) , statistical physics , computer science , random graph , complex network , mathematics , theoretical computer science , combinatorics , physics , mathematical analysis , graph , philosophy , epistemology , acoustics , machine learning
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.