Robustness of the in-degree exponent for the World-Wide Web.
Robustness of the in-degree exponent for the World-Wide Web.
复制标题
万维网入度指数的稳健性。
DOI：
--
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
H. Jeong
中科院分区：
文献类型：
--
作者：
B. Kahng;Y. Park;H. Jeong
我们考虑了一个有向无标度网络的随机模型，该模型在进出度分布中都遵循幂定律。在我们的模型中，顶点的数量以p的速度以几何级数的速度增长。在每个时间步，(I)每个新引入的顶点以与所选顶点的度内分布成线性比例的概率连接到固定数量的已有顶点，(Ii)每个现有顶点通过一个随机乘法过程更新其传出边，该过程具有传出边的平均增长率g及其方差σ(2)。通过解析处理和数值模拟，我们发现虽然出度指数伽马(OUT)依赖于参数，但入度指数伽马(In)有两个截然不同的值，p>；g的Gamma(In)=2，p<；g的1，与不同的参数值无关。后一种情况对幂定律进行了对数修正。由于现在的万维网(WWW)的顶点增长率p大于度增长率g，所以对于WWW，当Gamma(In)=2时，度指数表现得很稳健。
We consider a stochastic model for directed scale-free networks following power laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with a growth rate p. At each time step, (i) each newly introduced vertex is connected to a constant number of already existing vertices with the probability linearly proportional to in-degree distribution of a selected vertex, and (ii) each existing vertex updates its outgoing edges through a stochastic multiplicative process with mean growth rate of outgoing edges g and its variance sigma(2). Using both analytic treatment and numerical simulations, we show that while the out-degree exponent gamma(out) depends on the parameters, the in-degree exponent gamma(in) has two distinct values, gamma(in)=2 for p>g and 1 for p<g, independent of different parameters values. The latter case has logarithmic correction to the power law. Since the vertex growth rate p is larger than the degree growth rate g for the World-Wide Web (WWW) nowadays, the in-degree exponent appears robust as gamma(in)=2 for the WWW.
DOI：
10.1073/pnas.200327197
发表时间：
2000-10-10
影响因子：
11.1
作者：
Amaral, LAN;Scala, A;Stanley, HE
通讯作者：
Stanley, HE