复杂网络演化模型

●BA模型	网络增长、偏好连接
●基于蛋白质相互作用的演化模型	复制、分化、变异
●优化演化模型

Most real world networks have the same internal structure:

Scale-free networks

●其形成机制是什么？

BA偏好连接模型——PREFERENTIAL ATTACHMENT

(1)The number of nodes (N) is NOT fixed. 

Networks continuously expand by the addition of new nodes.

Examples:                                              

WWW : addition of new documents                   

Citation : publication of new papers

(2) The attachment is NOT uniform.

A node is linked with higher probability to a node that already has a large number of links.

Examples :                                                                            

 WWW :  new documents link to well known sites (CNN, YAHOO, NewYork Times, etc)         Citation : well cited papers are more likely to be cited again

Scale-free model

(1) GROWTH : 

At every timestep we add a new node with m edges (connected to the nodes already present in the system).

(2) PREFERENTIAL ATTACHMENT : 

The probability Π that a new node will be connected to node i depends on the connectivity ki of that node