复杂网络局部结构熵的非广延分析
Nonextensive analysis on the local structure entropy of complex networks
摘要：
局部结构熵是一种识别复杂网络中影响节点的新方法。本文在Tsallis熵的基础上提出了一种新的复杂网络局部结构熵的形式。熵指数$q$的大小会影响局域结构熵的性质。当$q$的值为0时，非广延局部结构熵退化为一种新的度中心性形式。当$q$的值等于1时，非广延局部结构熵退化为局部结构熵的存在形式。在非广延局部结构熵中，我们也找到了一个非广延阈值。当$q$的值大于非扩张阈值时，改变$q$的值对局域结构熵的性质没有影响，并且不同的复杂网络具有不同的非扩张阈值。结果表明，新的非广延局域结构熵是局域结构熵的推广。它比现有的更合理，更有用。
英文摘要：
The local structure entropy is a new method which is proposed to identify the influential nodes in the complex networks. In this paper a new form of the local structure entropy of the complex networks is proposed based on the Tsallis entropy. The value of the entropic index $q$ will influence the property of the local structure entropy. When the value of $q$ is equal to 0, the nonextensive local structure entropy is degenerated to a new form of the degree centrality. When the value of $q$ is equal to 1, the nonextensive local structure entropy is degenerated to the existing form of the local structure entropy. We also have find a nonextensive threshold value in the nonextensive local structure entropy. When the value of $q$ is bigger than the nonextensive threshold value, change the value of $q$ will has no influence on the property of the local structure entropy, and different complex networks have different nonextensive threshold value. The results in this paper show that the new nonextensive local structure entropy is a generalised of the local structure entropy. It is more reasonable and useful than the existing one.
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