复杂网络中一个重要概念是度分布有幂律尾部,为了确定几何增长网络的度指数,需要采用度的补分布。于是,产生了一个理论问题:对离散分布,补分布具有幂律尾部是否分布就有幂律尾部,反之分布具有幂律尾部是否补分布就有幂律尾部。经研究发现事实并非如此,通过引入渐变化函数,给出了分布与补分布同时具有幂律尾部的充分必要条件。
An important concept in complex networks is the degree distribution has a power-law tail. In order to determine the degree exponent of geometric growth networks, people need to use complementary degree distribution. Then, a theoretical problem is proposed: for discrete distributions, if complementary distribution has a power-law tail, distribution has a power-law tail, and vice versa. We found that this conclusion is not true in general. A necessary and sufficient condition that distribution and complementary distribution also has a power-law tail is given in this paper.
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