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Non-Linear Preferential Attachment
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Non-Linear Preferential Attachment : ウィキペディア英語版
Non-Linear Preferential Attachment

In network science preferential attachment means that nodes tend to connect to those nodes which have more links. If the network is growing and new nodes tend to connect to existing ones with linear probability in the degree of the existing nodes then preferential attachment leads to a scale-free network. If this probability is sub-linear then the network’s degree distribution is stretched exponential and hubs are much smaller than in a scale-free network. If this probability is super-linear then almost all nodes are connected to a few hubs. According to Kunegis, Blattner and Moser several online networks follow non-linear preferential attachment model. Communication networks and online contact networks are sub-linear while interaction networks are super-linear. The co-author network among scientists also shows the signs of sub-linear preferential attachment.
== Types of preferential attachment ==

For simplicity it can be assumed that the probability with which a new node connects to an existing one follows a power function of the existing nodes’ degree (k):
π(k) ~ kα
where α>0. This is a good approximation for a lot of real networks such as the Internet, the citation network or the actor network. If α=1 then the preferential attachment is linear. If α<1 then it is sub-linear while if α>1 then it is super-linear.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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